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Automation Scripts for Feeder Analysis using CymPy

SAND2025-00330O Automation Scripts for Feeder Analysis using CymPy is a software tool that uses Python scripts to automate the analysis of power system feeders using CYME software. Utilities and researchers can use it to perform various types of analyses by leveraging the capabilities of CYME. The scripts use the CymPy library to interface with CYME and automate the analysis process. The software uses standard Python libraries along with the Eaton CymPy library. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525

Reno, Matthew↗

NovaDemux v39.07

This program is a sequence demultiplexer intended primarily for, but not limited to, Illumina sequencing machines. Typically, multiple experiments ("libraries") are pooled together and sequenced at once, with genetic molecules of these libraries tagged with a synthetic DNA "barcode". After sequencing, the data is demultiplexed into one file per library based on the barcode. However, errors in barcode reading cause misassignment and decrease yield. NovaDemux uses advanced statistical methods to maximize yield while minimizing misassignment compared to existing software.

Bushnell, Brian [Lawrence Berkeley National Labora↗

radkit base v1.6

The radkit (base) software suite (python) consists of three primary libraries: stark, trajan, and curie. The trajan library provides the tools to analyze and manipulate data from lidar and inertial measurement unit (IMU) devices, cameras, as well as trajectories from algorithms such as simultaneous localization and mapping (SLAM). These components allow reading and writing standard data formats, performing rigid affine transformations, discretizing three-dimensional space, and visualizing data products. The curie library comprises a standard set of object-oriented tools for radiation data and analysis in the following modules: (1) listmode and binmode data classes with methods for manipulation, plotting, slicing and file IO; (2) radiological/nuclear source detection/identification analysis results; (3) source encounters of correlated analyses and (4) energy-dependent angular detector response functions. The stark package provides low-level tools that are leveraged by both curie and trajan. The tools are flexible for offline analysis as well as performant for real-time integrations.

Salathe, Marco [Lawrence Berkeley National Laborat↗

FAD-Toolset (Floating Array Design Toolset) [SWR-26-056]

The Floating Array Design (FAD) Toolset is a collection of tools for modeling and designing arrays of floating offshore structures. It was originally designed for floating wind systems but has applicability for many offshore applications. A core part of the FAD Toolset is the floating array model, which serves as a high-level library for efficiently modeling a floating array, such as a floating wind array. It combines site condition information and a description of the floating array design, and contains functions for evaluating the array's behavior considering the site conditions. For example, it combines information about site soil conditions, mooring line loads, and an array's anchor characteristics to estimate the holding capacity of each anchor. The library works in conjunction with the tools RAFT, MoorPy, and FLORIS to model floating platforms, wind turbines, mooring systems, power cables, and array wakes respectively. Layered on top of the floating array model is a set of design tools that can be used for algorithmically adjusting or optimizing parts of the a floating array. Specific tools existing for mooring lines, shared mooring systems, dynamic power cables, static power cable routing, and overall array layout. These capabilities work with the design representation and evaluation functions in the floating array model, and they can be applied by users in various combinations to suit different purposes. In addition to standalone uses of the FAD Toolset, a coupling has been made with Ard, (https://github.com/NLRWindSystems/Ard) a sophisticated and flexible wind farm optimization tool. This coupling allows Ard to use certain mooring system capabilities from FAD to perform layout optimization of floating wind farms with Ard's more advanced layout optimization capabilities. The FAD Toolset works with the IEA Wind Task 49 Ontology (https://github.com/IEAWindTask49/Ontology), which provides a standardized format for describing floating wind farm sites and designs. See example use cases in our examples folder (https://github.com/NLRWindSystems/FAD-Toolset/blob/main/examples/README.md) For working with the library, it is important to understand the floating array model structure, which is described more here: https://github.com/NLRWindSystems/FAD-Toolset/blob/main/fad/README.md.

Sirkis, Leah [National Laboratory of the Rockies (↗

torch-einshard v1.0

torch-einshard is a Python library for describing local and distributed PyTorch tensor computations with compact, einsum-like notation. Its expressions name logical axes, specify how they are sharded across a PyTorch DeviceMesh, and represent partial reductions. The library automatically performs contractions, permutations, reshaping, splitting, gathering, reduction, reduce-scatter, and repartitioning while preserving autograd. Additional features include sharding-aware FFTs, tensor rolls, halo exchange, sliding windows, 1D–3D convolutions, uneven-shard handling, parameter initialization and gradient management, and cost-based execution planning. It is designed for scientific machine learning and large-model workloads, including tensor-, sequence-, and spatial-parallel MLPs, attention, convolutions, and spectral operations. Compared with manually combining torch.einsum and distributed collectives, torch-einshard expresses both the mathematical operation and data placement in one readable formula. This reduces boilerplate and synchronization errors, keeps forward and backward communication consistent, and allows the library to select optimized collective strategies without changing model code.

Morozov, Dmitriy [Lawrence Berkeley National Labor↗

BoBa

BoBa is a C++ software library for working with large matrices, tensors, and tensor decompositions. The library provides tools for dense matrix and tensor operations, tensor decompositions, and tensor decomposition methods that support modern CPU and GPU architectures. It includes portable abstractions for linear algebra, tensor algebra, and multidimensional computation. BoBa is intended for scientific computing applications that involve large multidimensional data sets or high dimensional mathematical models. Its capabilities support tasks such as data compression, linear algebra, efficient numerical computation, and the development of scalable algorithms for heterogeneous hardware. Tutorials, tests, and example applications are included to help users learn and apply the library.

Yao, Jin [Lawrence Livermore National Laboratory (↗

TensorFEM

The purpose of this research library is to demonstrate how to combine the BoBa tensor library and MFEM finite element library to enable tensorized finite element methods.

Guthrey, PiersonT [Lawrence Livermore National Lab↗

HDF5 in the exascale era: Delivering efficient and scalable parallel I/O for exascale applications

Accurately modeling real-world systems requires scientific applications at exascale to generate massive amounts of data and manage data storage efficiently. However, parallel input and output (I/O) faces challenges due to new application workflows and the state-of-the-art memory, interconnect, and storage architectures considered in exascale designs. The storage hierarchy has expanded with node-local persistent memory, solid-state storage, and traditional disk and tape-based storage, thus requiring efficiency at each layer and much more efficient data movement among these layers. This paper discusses how the ExaHDF5 project improved the I/O performance and data management for exascale architectures by enhancing HDF5, a widely used parallel I/O library. The team developed an Asynchronous I/O Virtual Object Layer (VOL) connector that allowed overlapping I/O with computation. They also created a Cache VOL to complement asynchronous I/O by incorporating fast storage layers, such as burst buffer and node-local storage, into the parallel I/O workflow through caching and staging data. Additionally, the team enabled data aggregation and I/O at the node level by using a Subfiling Virtual File Driver (VFD). To demonstrate superior I/O performance with HDF5 at exascale, the ExaHDF5 team collaborated with several exascale applications. In this paper, we show I/O performance improvements for three applications: Cabana (a particle-based simulation library), EQSIM (a regional earthquake simulation software), and E3SM (a climate system modeling library).

Asynchronous I/Ol↗

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗

PETSc/TAO developments for GPU-based early exascale systems

The Portable Extensible Toolkit for Scientific Computation (PETSc) library provides scalable solvers for nonlinear time-dependent differential and algebraic equations and for numerical optimization via the Toolkit for Advanced Optimization (TAO). PETSc is used in dozens of scientific fields and is an important building block for many simulation codes. During the U.S. Department of Energy’s Exascale Computing Project, the PETSc team has made substantial efforts to enable efficient utilization of the massive fine-grain parallelism present within exascale compute nodes and to enable performance portability across exascale architectures. We recap some of the challenges that designers of numerical libraries face in such an endeavor, and then discuss the many developments we have made, which include the addition of new GPU backends, features supporting efficient on-device matrix assembly, better support for asynchronicity and GPU kernel concurrency, and new communication infrastructure. In conclusion, we evaluate the performance of these developments on some pre-exascale systems as well as the early exascale systems Frontier and Aurora, using compute kernel, communication layer, solver, and mini-application benchmark studies, and then close with a few observations drawn from our experiences on the tension between portable performance and other goals of numerical libraries.

Exascale Computing Project (ECP)↗

Preparing MPICH for exascale

The advent of exascale supercomputers heralds a new era of scientific discovery, yet it introduces significant architectural challenges that must be overcome for MPI applications to fully exploit its potential. Among these challenges is the adoption of heterogeneous architectures, particularly the integration of GPUs to accelerate computation. Additionally, the complexity of multithreaded programming models has also become a critical factor in achieving performance at scale. The efficient utilization of hardware acceleration for communication, provided by modern NICs, is also essential for achieving low latency and high throughput communication in such complex systems. In response to these challenges, the MPICH library, a high-performance and widely used Message Passing Interface (MPI) implementation, has undergone significant enhancements. Here, this paper presents four major contributions that prepare MPICH for the exascale transition. First, we describe a lightweight communication stack that leverages the advanced features of modern NICs to maximize hardware acceleration. Second, our work showcases a highly scalable multithreaded communication model that addresses the complexities of concurrent environments. Third, we introduce GPU-aware communication capabilities that optimize data movement in GPU-integrated systems. Finally, we present a new datatype engine aimed at accelerating the use of MPI derived datatypes on GPUs. These improvements in the MPICH library not only address the immediate needs of exascale computing architectures but also set a foundation for exploiting future innovations in high-performance computing. By embracing these new designs and approaches, MPICH-derived libraries from HPE Cray and Intel were able to achieve real exascale performance on OLCF Frontier and ALCF Aurora respectively.

Guo, Yanfei [Argonne National Laboratory (ANL), Ar↗

CRISPR-mediated multigene integration enables Shikimate pathway refactoring for enhanced 2-phenylethanol biosynthesis in Kluyveromyces marxianus

Background: 2-phenylethanol (2-PE) is a rose-scented flavor and fragrance compound that is used in food, beverages, and personal care products. Compatibility with gasoline also makes it a potential biofuel or fuel additive. A biochemical process converting glucose or other fermentable sugars to 2-PE can potentially provide a more sustainable and economical production route than current methods that use chemical synthesis and/or isolation from plant material. Results: We work toward this goal by engineering the Shikimate and Ehrlich pathways in the stress-tolerant yeast Kluyveromyces marxianus. First, we develop a multigene integration tool that uses CRISPR-Cas9 induced breaks on the genome as a selection for the one-step integration of an insert that encodes one, two, or three gene expression cassettes. Integration of a 5-kbp insert containing three overexpression cassettes successfully occurs with an efficiency of 51 ± 9% at the ABZ1 locus and was used to create a library of K. marxianus CBS 6556 strains with refactored Shikimate pathway genes. The 3 3 -factorial library includes all combinations of KmARO4, KmARO7, and KmPHA2, each driven by three different promoters that span a wide expression range. Analysis of the refactored pathway library reveals that high expression of the tyrosine-deregulated KmARO4 K221L and native KmPHA2, with the medium expression of feedback insensitive KmARO7 G141S , results in the highest increase in 2-PE biosynthesis, producing 684 ± 73 mg/L. Ehrlich pathway engineering by overexpression of KmARO10 and disruption of KmEAT1 further increases 2-PE production to 766 ± 6 mg/L. The best strain achieves 1943 ± 63 mg/L 2-PE after 120 h fed-batch operation in shake flask cultures. Conclusions: The CRISPR-mediated multigene integration system expands the genome-editing toolset for K. marxianus, a promising multi-stress tolerant host for the biosynthesis of 2-PE and other aromatic compounds derived from the Shikimate pathway.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On-the-fly response function generation method for composite coarse mesh

The hybrid stochastic deterministic transport code COMET, based on the incident response expansion theory, is used to model reactor cores with high fidelity and formidable computational speed. COMET models a reactor core using a library of incident flux response expansion coefficients that are pre computed for all the unique lattice cells (e.g., fuel assemblies, reflector blocks, etc.) in the core. In order to further improve its computational efficiency in pre-calculating the response library a new response function generation method is developed to compute the response functions for the composite coarse meshes made of a smaller set of unique lattices on the fly within the COMET's deterministic transport core sweep. The efficiency is achieved by eliminating a number of unique lattices that can be made up from the reduced set of unique meshes on the fly. The numerical process consists of the following steps. First, the boundary condition on composite coarse mesh boundaries is projected onto the expansion basis to compute the incident flux moments on external surfaces of all the basic (reduced set of unique) coarse meshes. Secondly, the deterministic sweeping solver in COMET is used to converge on the outgoing/incoming flux expansion moments crossing interfaces between the basic coarse meshes. Thirdly, the response functions for the composite coarse meshes are constructed as a superposition on the fly. The new response function generation method was tested on 88 composite coarse meshes consisting of CANDU fuel bundles and moderator blocks. It was found that response functions generated by the new method agree very well with those generated by direct Monte Carlo calculations. The average and maximum relative differences in the surface-to-surface response coefficients computed by the two methods are 0.10% and 0.20%, respectively. Similarly, the average and maximum relative differences in the response fission densities are 0.13% and 0.43%, respectively. These discrepancies are within one standard deviation of the stochastic uncertainties. The new method is five times faster than the original direct Monte Carlo method. The size of the response function library for the new method is five times smaller than that for the original method, leading to significantly less requirement for the computer hard drive space and memory. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Analysis of SCALE Criticality and Sensitivity Calculations for Reflected HEU Cylinders

The SCALE code package offers multiple nuclear data libraries and sensitivity and uncertainty (S/U) methods supporting and derived from Monte Carlo (MC) transport. The CSAS and TSUNAMI-3D sequences use KENO MC, utilizing either continuous-energy (CE) cross sections or multigroup (MG) cross section libraries. TSUNAMI-3D has two CE calculational methods: the iterated fission probability (IFP) method, and the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method. Previous work has shown poor agreement between CLUTCH and confirmatory direct perturbation calculations in specific applications (e.g., fissionable and polyethylene reflectors). The HEU-MET-FAST-084 (HMF-084) International Criticality Safety Benchmark Evaluation Project evaluation consists of 27 cylindrical highly enriched uranium metal cores with 14 unique reflector materials of 0.5 and 1 in. thicknesses. Included in this list of reflector materials are natural uranium and polyethylene. This work utilized SCALE 6.2.4 models of the HMF-084 evaluation, with additional non-physical configurations to test both the MG bias and CLUTCH functionality across a variety of reflector material thicknesses. The evaluation’s use of concentric cylinders allowed for examination of several MG self-shielding methods: infinite homogenous, cylindrical, and spherical. The results indicate that the use of polyethylene reflectors with CLUTCH is not fundamentally impossible but sensitive to geometry. The poor performance of CLUTCH with fissionable reflectors was reaffirmed. The 2 in. and greater polyethylene-reflected calculations demonstrate the necessity of using the 302-group library for fast systems. The nickel MG bias was substantial, as discussed in a companion paper, as were cobalt and iron.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Discovery of photosynthesis genes through whole-genome sequencing of acetate-requiring mutants of Chlamydomonas reinhardtii

Large-scale mutant libraries have been indispensable for genetic studies, and the development of next-generation genome sequencing technologies has greatly advanced efforts to analyze mutants. In this work, we sequenced the genomes of 660 Chlamydomonas reinhardtii acetate-requiring mutants, part of a larger photosynthesis mutant collection previously generated by insertional mutagenesis with a linearized plasmid. We identified 554 insertion events from 509 mutants by mapping the plasmid insertion sites through paired-end sequences, in which one end aligned to the plasmid and the other to a chromosomal location. Nearly all (96%) of the events were associated with deletions, duplications, or more complex rearrangements of genomic DNA at the sites of plasmid insertion, and together with deletions that were unassociated with a plasmid insertion, 1470 genes were identified to be affected. Functional annotations of these genes were enriched in those related to photosynthesis, signaling, and tetrapyrrole synthesis as would be expected from a library enriched for photosynthesis mutants. Systematic manual analysis of the disrupted genes for each mutant generated a list of 253 higher-confidence candidate photosynthesis genes, and we experimentally validated two genes that are essential for photoautotrophic growth, CrLPA3 and CrPSBP4 . The inventory of candidate genes includes 53 genes from a phylogenomically defined set of conserved genes in green algae and plants. Altogether, 70 candidate genes encode proteins with previously characterized functions in photosynthesis in Chlamydomonas , land plants, and/or cyanobacteria; 14 genes encode proteins previously shown to have functions unrelated to photosynthesis. Among the remaining 169 uncharacterized genes, 38 genes encode proteins without any functional annotation, signifying that our results connect a function related to photosynthesis to these previously unknown proteins. This mutant library, with genome sequences that reveal the molecular extent of the chromosomal lesions and resulting higher-confidence candidate genes, will aid in advancing gene discovery and protein functional analysis in photosynthesis.

59 BASIC BIOLOGICAL SCIENCES↗

cppTPSA/pyTPSA: a C++/Python package for truncated power series algebra

The truncated power series algebra (TPSA), also referred to as differential algebra (DA), is a well-established and widely used method in particle accelerator physics and astronomy. The most straightforward usage of TPSA/DA is to calculate the Taylor expansion of a given function at a specific point up to order ?. In recent years, as the application of TPSA/TA has been extended to other fields, a reusable implementation of TPSA/DA as a modern C++ library or other high level programming language like Python has become desirable. The cppTPSA package implements TPSA/DA in C++11 and provides developers a convenient library with which to build advanced TPSA/DA-based methods. A Python 3 library, pyTPSA, has also been developed based on the C++ lib.

97 MATHEMATICS AND COMPUTING↗

PeleLMeX: an AMR Low Mach Number Reactive Flow Simulation Code without level sub-cycling

PeleLMeX simulates chemically reacting low Mach number flows with block-structured adaptive mesh refinement (AMR). The code is built upon the AMReX library, which provides the underlying data structures and tools to manage and operate on them across massively parallel computing architectures. PeleLMeX algorithmic features are inherited from its predecessor PeleLM but key improvements allow representation of more complex physical processes. Together with its compressible flow counterpart PeleC, the thermo-chemistry library PelePhysics and the multi-physics library PeleMP, it forms the Pele suite of open-source reactive flow simulation codes.

97 MATHEMATICS AND COMPUTING↗

A Systems Biology Approach to Energy Flow in H 2 Producing Microbial Communities: Microbial Mats

This report describes the results of work conducted at NASA Ames Research Center, in collaboration with investigators at Lawrence Livermore National Laboratory, during the time period 12/15/2014 to 12/15/2017. The work was an extension of a collaboration with LLNL that began in 2008. Work this reporting period focused primarily on tasks related to microbial mats from both the Elkhorn Slough and Baja California field sites, including the analysis and publication of data produced prior to 12/15/2014. During this reporting period, in addition to the microbial mat work, we also conducted a series of experiments with a particular algal-bacterial association (C. sorokiniana and A. brasilense). A number of aspects of this well-characterized algal-bacterial association enabled us not only to further our understanding of interactions between these particular organisms, but to apply that knowledge and techniques to our collection of microorganisms isolated from microbial mats. Microbial mat experiments focused both on intact mat communities and on cultures of organisms isolated from the mats (the Microbial Mat Living Library). In a series of co-culture experiments, we documented both positive and negative interactions amongst heterotrophic and autotrophic isolates of microbial mat microorganisms. One particularly important and novel mat cyanobacterium (ESFC-1) was studied in detail. We developed techniques to pursue an investigation of functional redundancy (the idea that closely related organisms perform identical roles in a community) in cyanobacterial autotrophs in the Elkhorn Slough microbial mat. In those experiments, we documented numerous instances of increases in growth rate between co-cultures of two organisms (relative to their growth rate in isolation) performing what would seem to be identical functional roles. Simplified microbial mat communities consisting of organisms from the Microbial Mat Living Library were constructed and studied in laboratory experiments. The “constructed mats” were grown in standard laboratory glassware and plasticware, but cultures were also combined with artificial materials in an effort to re-create the three-dimensional structure of naturally occurring microbial mats. These constructed mats re-created a number of functions attributable to natural microbial mats (N-fixation, H2-production) and simplified their study using molecular ecological techniques due to the smaller number of microbial “species” present. Cyanobacteria which migrated in response to vertical variations in light intensity (irradiance) obtained characteristic positions in constructed mats that were similar to their positions in natural mats. A detailed investigation of nitrogen cycling in both the Baja California and Elkhorn Slough microbial mats was initiated during this reporting period. The nitrogen cycle in the microbial mats has not been studied in depth, despite the fact that nitrogen usually limits growth in marine environments. The organisms conducting nitrogen cycling in both microbial mats were studied using the genomes available from earlier work on these mats, as well as with a targeted approach using molecular ecological methods developed here. Quantitative measurements of rates of nitrogen transformations were made using stable isotopically labeled nitrogen. The processes quantified and examined using molecular ecological methods included: nitrogen fixation, ammonification, ammonium and nitrate assimilation, denitrification, anaerobic oxidation of ammonium, and dissimilatory nitrate reduction to ammonium. In a series of experiments designed to examine a potential application for microbial mats, we demonstrated that both Elkhorn Slough and Baja California microbial mats were very effective in removing large quantities of both nitrate and ammonium from waste streams containing these compounds at levels where they would be considered to be pollutants. Considerable effort was expended during this reporting period to analyze, and prepare for publication, metagenomes and metatranscriptomes collected from two experimental manipulations of microbial mats. The first, a diel study, was conducted in November 2011, while the second, an investigation of the effects of sulfate on community composition, was conducted during this reporting period. For the earlier study, reference-based and reference-free methods were used to assess microbial ecology and genetic partitioning in these complex microbial systems, and that work is available as a pre-print. Four metagenomes from the same experiment were published. In the second, longer (nearly 200 day) manipulation, rRNA iTag libraries for cDNA and DNA were analyzed to determine the effects of sulfate concentration on microbial mat community composition over the course of the experiment. Work on the algal-bacterial association (Chlorella sorokiniana and Azospirillum brasilense) focused initially on demonstrating the transfer of carbon and nitrogen between the partners, using stable isotopic labeling and the LLNL NanoSIMS. Subsequently, the potential role of diazotrophy (nitrogen fixation) by the bacterial partner in supporting the growth of the association was assessed in a series of experiments. It appears to be the case that, although the bacterial partner demonstrably increases the fitness of the algae under nitrogen limitation, and cells of C. sorokiniana receive nitrogen originally fixed from atmospheric nitrogen by A. brasilense, the amount of nitrogen obtained by diazotrophy is too small to explain the increase in fitness.

08 HYDROGEN↗