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At least 109 records · Page 6

MINE: a new way to design genetics experiments for discovery

Abstract The Maximally Informative Next Experiment or MINE is a new experimental design approach for experiments, such as those in omics, in which the number of effects or parameters p greatly exceeds the number of samples n (p > n). Classical experimental design presumes n > p for inference about parameters and its application to p > n can lead to over-fitting. To overcome p > n, MINE is an ensemble method, which makes predictions about future experiments from an existing ensemble of models consistent with available data in order to select the most informative next experiment. Its advantages are in exploration of the data for new relationships with n < p and being able to integrate smaller and more tractable experiments to replace adaptively one large classic experiment as discoveries are made. Thus, using MINE is model-guided and adaptive over time in a large omics study. Here, MINE is illustrated in two distinct multiyear experiments, one involving genetic networks in Neurospora crassa and a second one involving a genome-wide association study in Sorghum bicolor as a comparison to classic experimental design in an agricultural setting.

Biochemistry & Molecular Biology↗

An Open-Science Approach to Address Individual Response to Simulated GCR In Genetically Diverse Populations of Mice and Humans

This project addresses the challenge of understanding and predicting individual radiation sensitivity by integrating genetics, demographics and biomarker characteristics across species (mice and humans). We hypothesize that ex vivo DNA repair response to GCR components is a central determinant of cancer risk from space radiation and can serve as a biomarker of radiation risk in combination with genetics. Automated image quantification of 53BP1+ radiation-induced foci (RIF) during the first 4-48 h post-irradiation was performed as a function of dose and LET in non-immortalized primary skin fibroblasts derived from 76 mice across 15 strains (5 inbred reference strains and 10 collaborative-cross strains) exposed to X rays (0.1, 1 and 4 Gy), 350 MeV/n 40Ar and 600 MeV/n 56Fe (1.1 and 3 particles/100sq. μm), as well as in peripheral blood mononuclear cells (PBMCs) from 768 healthy donors (matched ethnicity, 50/50 male/female, 18-70 years old) exposed to gamma rays (0.1 and 1 Gy), 350 MeV/n 28Si, 350 MeV/n 40Ar and 600 MeV/n 56Fe (1.1 and 3 particles/100sq. μm). A genome-wide association study (GWAS) was performed on the mouse strains between DNA damage responses to space radiation and single nucleotide polymorphisms (SNPs). We found SNPs, which were significantly associated to the RIF phenotype, mapped to genes and pathways that are functionally linked to health hazards for deep space exploration (e.g. carcinogenesis, nervous system damage and immune dysfunction). Some of these SNPs were located within protein coding regions, potentially interfering with protein functions and providing promising genetic targets for countermeasures. We also found correlations between both spontaneous and radiation-induced DNA damage and SNPs mapped to pathways associated with cellular metabolism. GWAS is undergoing for the human data. All data have been made available via the NASA Space Biology Open-Science database (genelab.nasa.gov) and we will discuss how various genomic and transcriptomic datasets can be accessed for modeling and integrated using machine learning methods for discovering new radiation biology.

Sylvain V Costes↗

Conserved defense responses between maize and sorghum to Exserohilum turcicum

Abstract Background Exserohilum turcicum is an important pathogen of both sorghum and maize, causing sorghum leaf blight and northern corn leaf blight. Because the same pathogen can infect and cause major losses for two of the most important grain crops, it is an ideal pathosystem to study plant-pathogen evolution and investigate shared resistance mechanisms between the two plant species . To identify sorghum genes involved in the E. turcicum response, we conducted a genome-wide association study (GWAS). Results Using the sorghum conversion panel evaluated across three environments, we identified a total of 216 significant markers. Based on physical linkage with the significant markers, we detected a total of 113 unique candidate genes, some with known roles in plant defense. Also, we compared maize genes known to play a role in resistance to E. turcicum with the association mapping results and found evidence of genes conferring resistance in both crops, providing evidence of shared resistance between maize and sorghum . Conclusions Using a genetics approach, we identified shared genetic regions conferring resistance to E. turcicum in both maize and sorghum. We identified several promising candidate genes for resistance to leaf blight in sorghum, including genes related to R-gene mediated resistance. We present significant advancements in the understanding of host resistance to E. turcicum , which is crucial to reduce losses due to this important pathogen.

59 BASIC BIOLOGICAL SCIENCES↗

Assessing and Improving Biooxidation for Acid Generation and Rare Earth Element Extraction

Microorganisms (Acidithiobacillus ferrooxidanns) are effective in oxidizing ferrous ions that can be used to oxidize pyrite and produce sulfuric acid. Many coal waste resources contain significant concentrations of rare earth elements (REE) and critical materials (CM) that can be extracted using sulfuric acid. These coal waste resources often contain significant concentrations of pyrite, which if not utilized or removed present a future environmental liability for potential acid mine drainage. Thus, the combination of pyrite and REE/CM in coal waste provides a significant resource opportunity for sulfuric acid generation that can be utilized using biooxidation. In addition, the pyrite concentrate used for acid generation also contains REE/CM content that is released during biooxidation of the pyrite concentrate that augments the REE/CM release from the main ore being leached with the acid generated from the pyrite. Thus, this approach provides a very significant environmental advantage as well as augmented REE/CM recovery. Although there are many studies associated with biooxidation in relation to mineral oxidation, there is a lack of information regarding the effects of operating parameters on biooxidation performance and optimization for practical applications. In this study, findings from research in assessing and improving biooxidation for acid generation for REE/CM extraction are presented. Results show that bacteria can very effectively and efficiently oxidize ferrous ions to ferric ions, which oxidize pyrite to produce acid for REE/CM extraction. The factors that showed significant impact on biooxidation performance include air flow rate, stirring speed, residence time, solids concentration, and temperature. The dominance of Leptospirillum ferriphilum species was noted in the bioreactor after a prolonged period of operation, although Acidithiobacillus ferrooxidanns was used in the beginning.

Free, Michael L.↗

Evaluation of genetic diversity, agronomic traits, and anthracnose resistance in the NPGS Sudan Sorghum Core collection

The United States Department of Agriculture (USDA) National Plant Germplasm System (NPGS) sorghum core collection contains 3011 accessions randomly selected from 77 countries. Genomic and phenotypic characterization of this core collection is necessary to encourage and facilitate its utilization in breeding programs and to improve conservation efforts. In this study, we examined the genome sequences of 318 accessions belonging to the NPGS Sudan sorghum core set, and characterized their agronomic traits and anthracnose resistance response. We identified 183,144 single nucleotide polymorphisms (SNPs) located within or in proximity of 25,124 annotated genes using the genotyping-by-sequencing (GBS) approach. The core collection was genetically highly diverse, with an average pairwise genetic distance of 0.76 among accessions. Population structure and cluster analysis revealed five ancestral populations within the Sudan core set, with moderate to high level of genetic differentiation. In total, 171 accessions (54%) were assigned to one of these populations, which covered 96% of the total genomic variation. Genome scan based on Tajima’s D values revealed two populations under balancing selection. Phenotypic analysis showed differences in agronomic traits among the populations, suggesting that these populations belong to different ecogeographical regions. A total of 55 accessions were resistant to anthracnose; these accessions could represent multiple resistance sources. Genome-wide association study based on fixed and random model Circulating Probability (farmCPU) identified genomic regions associated with plant height, flowering time, panicle length and diameter, and anthracnose resistance response. Integrated analysis of the Sudan core set and sorghum association panel indicated that a large portion of the genetic variation in the Sudan core set might be present in breeding programs but remains unexploited within some clusters of accessions. The NPGS Sudan core collection comprises genetically and phenotypically diverse germplasm with multiple anthracnose resistance sources. Population genomic analysis could be used to improve screening efforts and identify the most valuable germplasm for breeding programs. The new GBS data set generated in this study represents a novel genomic resource for plant breeders interested in mining the genetic diversity of the NPGS sorghum collection.

59 BASIC BIOLOGICAL SCIENCES↗

A multifunctional sesquiterpene synthase integrates with cytochrome P450s to reinforce the terpenoid defense network in maize

Terpenoids, the largest and most structurally diverse class of plant natural products, play essential roles in maize defense and ecological interactions. In this study, we identified and functionally characterized a sesquiterpenoid-based defense pathway in maize centered on α-santalenoic acid, a pathogen-inducible sesquiterpenoid antibiotic. Using a combination of metabolite-based genome-wide association studies (mGWAS), linkage mapping, and heterologous expression assays, we identified ZmTPS9 as a multiproduct terpene synthase that primarily produces α-santalene and β-bisabolene. Sequence analysis and site-directed mutagenesis revealed that threonine at position 413 is critical for enzyme activity, with its deletion resulting in a complete loss of enzyme activity. The sesquiterpene hydrocarbons produced by ZmTPS9 are further oxidized by three cytochrome P450 monooxygenases, ZmCYP71Z16, ZmCYP71Z18, and ZmCYP71Z19, to yield antimicrobial metabolites including α-santalenoic acid, zealexin D1 (ZD1), and zealexin D2 (ZD2). Together, these findings demonstrate a convergent biosynthetic strategy in maize, where multiproduct terpene synthases and promiscuous P450s collaboratively generate a flexible and robust terpenoid defense network.

a-santalenoic acid↗

Case studies of robots and automation as health/safety interventions in small manufacturing enterprises

This article reviews the experiences of 63 case studies of small businesses (<250 employees) with manufacturing automation equipment acquired through a health/safety intervention grant program. The review scope included equipment technologies classified as industrial robots (n = 17), computer numerical control (CNC) machining (n = 29), or other programmable automation systems (n = 17). Descriptions of workers' compensation (WC) claim injuries and identified risk factors that motivated the acquisition of the equipment were extracted from grant applications. Other aspects of the employer experiences, including qualitative and quantitative assessment of effects on risk factors for musculoskeletal disorders (MSD), effects on productivity, and employee acceptance of the intervention were summarized from the case study reports. Case studies associated with a combination of large reduction in risk factors, lower cost per affected employee, and reported increases in productivity were CNC stone cutting system, CNC/vertical machining system, automated system for bottling, CNC/routing system for plastics products manufacturing, and a CNC/Cutting system for vinyl/carpet. Six case studies of industrial robots reported quantitative reductions in MSD risk factors in these diverse manufacturing industries: snack foods; photographic film, paper, plate, and chemical; machine shops; leather goods and allied products; plastic products; and iron and steel forging. Furthermore, this review of health/safety intervention case studies indicates that advanced (programmable) manufacturing automation, including industrial robots, reduced workplace musculoskeletal risk factors, and improved process productivity in most cases.

42 ENGINEERING↗

Genomic Analysis of the Natural Variation of Fatty Acid Composition in Seed Oils of Camelina sativa

Camelina sativa is an oilseed crop that has shown strong promise as a biofuel feedstock. The profile of fatty acids greatly influences the oil quality; however, genetic mechanisms that determine the natural variation of fatty acid composition in camelina are not fully understood. A genome wide association study (GWAS) was performed to uncover genetic loci that may contribute to the contents of major fatty acids such as oleic and linolenic acids in camelina seed. Two approaches were taken to improve the GWAS efficiency. First, growing a diversity panel of 212 accessions in four locations and two nitrogen fertilization conditions revealed great variation in fatty acid contents in seeds. Second, using an improved reference genome, abundant markers, including 203,320 single nucleotide polymorphisms (SNPs) and 99,067 insertions/deletions (indels), were developed, which refined the population structure of the diversity panel. GWAS resulted in 118 genetic markers across 31 trait/treatment conditions. Closely linked markers were determined based on linkage decay and by comparing secondarily associated markers when highly associated ones were removed. Candidate genes were examined by comparing the pangenomes of 12 high-quality reference genomes. This study provides new resources to understand seed lipid metabolism and improve camelina oils through molecular breeding.

Life Sciences & Biomedicine - Other Topics↗

Identification of pleiotropic loci mediating structural and non-structural carbohydrate accumulation within the sorghum bioenergy association panel using high-throughput markers

Molecular characterization of diverse germplasm can contribute to breeding programs by increasing genetic gain for sorghum [ Sorghum bicolor (L.) Moench] improvement. Identifying novel marker-trait associations and candidate genes enriches the existing genomic resources and can improve bioenergy-related traits using genomic-assisted breeding. In the current scenario, identifying the genetic loci underlying biomass and carbon partitioning is vital for ongoing efforts to maximize each carbon sink’s yield for bioenergy production. Here, we have processed a high-density genomic marker (22 466 550) data based on whole-genome sequencing (WGS) using a set of 365 accessions from the bioenergy association panel (BAP), which includes ~19.7 million (19 744 726) single nucleotide polymorphism (SNPs) and 2.7 million (~2 721 824) insertion deletions (indels). A set of high-quality filtered SNP (~5.48 million) derived markers facilitated the assessment of population structure, genetic diversity, and genome-wide association studies (GWAS) for various traits related to biomass and its composition using the BAP. The phenotypic traits for GWAS included seed color (SC), plant height (PH), days to harvest (DTH), fresh weight (FW), dry weight (DW), brix content % (BRX), neutral detergent fiber (NDF), acid detergent fiber (ADF), non-fibrous carbohydrate (NFC), and lignin content. Several novel loci and candidate genes were identified for bioenergy-related traits, and some well-characterized genes for plant height ( Dw1 and Dw2 ) and the YELLOW SEED1 locus ( Y1 ) were validated. We further performed a multi-variate adaptive shrinkage analysis to identify pleiotropic QTL, which resulted in several shared marker-trait associations among bioenergy and compositional traits. Significant marker-trait associations with pleiotropic effects can be used to develop molecular markers for trait improvement using a marker-assisted breeding approach. Significant nucleotide diversity and heterozygosity were observed between photoperiod-sensitive and insensitive individuals of the panel. This diverse bioenergy panel with genomic resources will provide an excellent opportunity for further genetic studies, including selecting parental lines for superior hybrid development to improve biomass-related traits in sorghum.

bioenergy association panel↗

Transcription factor bHLH121 regulates root cortical aerenchyma formation in maize

Root anatomical phenotypes present a promising yet underexploited avenue to deliver major improvements in yield and climate resilience of crops by improving water and nutrient uptake. For instance, the formation of root cortical aerenchyma (RCA) significantly increases soil exploration and resource capture by reducing the metabolic costs of root tissue. A key bottleneck in studying such phenotypes has been the lack of robust high-throughput anatomical phenotyping platforms. We exploited a phenotyping approach based on laser ablation tomography, termed Anatomics , to quantify variation in RCA formation of 436 diverse maize lines in the field. Results revealed a significant and heritable variation for RCA formation. Genome-wide association studies identified a single-nucleotide polymorphism mapping to a root cortex-expressed gene-encoding transcription factor bHLH121. Functional studies identified that the bHLH121 Mu transposon mutant line and CRISPR/Cas9 loss-of-function mutant line showed reduced RCA formation, whereas an overexpression line exhibited significantly greater RCA formation when compared to the wild-type line. Characterization of these lines under suboptimal water and nitrogen availability in multiple soil environments revealed that bHLH121 is required for RCA formation developmentally as well as under studied abiotic stress. Overall functional validation of the bHLH121 gene’s importance in RCA formation provides a functional marker to select varieties with improved soil exploration and thus yield under suboptimal conditions.

59 BASIC BIOLOGICAL SCIENCES↗

Comprehensive analyses of 723 transcriptomes enhance genetic and biological interpretations for complex traits in cattle

By uniformly analyzing 723 RNA-seq data from 91 tissues and cell types, we built a comprehensive gene atlas and studied tissue specificity of genes in cattle. We demonstrated that tissue-specific genes significantly reflected the tissue-relevant biology, showing distinct promoter methylation and evolution patterns (e.g., brain-specific genes evolve slowest, whereas testisspecific genes evolve fastest). Through integrative analyses of those tissue-specific genes with large-scale genome-wide association studies, we detected relevant tissues/cell types and candidate genes for 45 economically important traits in cattle, including blood/immune system (e.g., CCDC88C) for male fertility, brain (e.g., TRIM46 and RAB6A) for milk production, and multiple growth-related tissues (e.g., FGF6 and CCND2) for body conformation. We validated these findings by using epigenomic data across major somatic tissues and sperm. Collectively, our findings provided novel insights into the genetic and biological mechanisms underlying complex traits in cattle, and our transcriptome atlas can serve as a primary source for biological interpretation, functional validation, studies of adaptive evolution, and genomic improvement in livestock.

59 BASIC BIOLOGICAL SCIENCES↗

COMPILE: a GWAS computational pipeline for gene discovery in complex genomes

Abstract Background Genome-Wide Association Studies (GWAS) are used to identify genes and alleles that contribute to quantitative traits in large and genetically diverse populations. However, traits with complex genetic architectures create an enormous computational load for discovery of candidate genes with acceptable statistical certainty. We developed a streamlined computational pipeline for GWAS (COMPILE) to accelerate identification and annotation of candidate maize genes associated with a quantitative trait, and then matches maize genes to their closest rice and Arabidopsis homologs by sequence similarity. Results COMPILE executed GWAS using a Mixed Linear Model that incorporated, without compression, recent advancements in population structure control, then linked significant Quantitative Trait Loci (QTL) to candidate genes and RNA regulatory elements contained in any genome. COMPILE was validated using published data to identify QTL associated with the traits of α-tocopherol biosynthesis and flowering time, and identified published candidate genes as well as additional genes and non-coding RNAs. We then applied COMPILE to 274 genotypes of the maize Goodman Association Panel to identify candidate loci contributing to resistance of maize stems to penetration by larvae of the European Corn Borer ( Ostrinia nubilalis ). Candidate genes included those that encode a gene of unknown function, WRKY and MYB-like transcriptional factors, receptor-kinase signaling, riboflavin synthesis, nucleotide-sugar interconversion, and prolyl hydroxylation. Expression of the gene of unknown function has been associated with pathogen stress in maize and in rice homologs closest in sequence identity. Conclusions The relative speed of data analysis using COMPILE allowed comparison of population size and compression. Limitations in population size and diversity are major constraints for a trait and are not overcome by increasing marker density. COMPILE is customizable and is readily adaptable for application to species with robust genomic and proteome databases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Genomic Dissection of Anthracnose ( Colletotrichum sublineolum ) Resistance Response in Sorghum Differential Line SC112-14

Sorghum production is expanding to warmer and more humid regions where its production is being limited by multiple fungal pathogens. Anthracnose, caused by Colletotrichum sublineolum , is one of the major diseases in these regions, where it can cause yield losses of both grain and biomass. In this study, 114 recombinant inbred lines (RILs) derived from resistant sorghum line SC112-14 were evaluated at four distinct geographic locations in the United States for response to anthracnose. A genome scan using a high-density linkage map of 3,838 single nucleotide polymorphisms (SNPs) detected two loci at 5.25 and 1.18 Mb on chromosomes 5 and 6, respectively, that explain up to 59% and 44% of the observed phenotypic variation. A bin-mapping approach using a subset of 31 highly informative RILs was employed to determine the disease response to inoculation with ten anthracnose pathotypes in the greenhouse. A genome scan showed that the 5.25 Mb region on chromosome 5 is associated with a resistance response to nine pathotypes. Five SNP markers were developed and used to fine map the locus on chromosome 5 by evaluating 1,500 segregating F 2:3 progenies. Based on the genotypic and phenotypic analyses of 11 recombinants, the locus was narrowed down to a 470-kb genomic region. Following a genome-wide association study based on 574 accessions previously phenotyped and genotyped, the resistance locus was delimited to a 34-kb genomic interval with five candidate genes. All five candidate genes encode proteins associated with plant immune systems, suggesting they may act in synergy in the resistance response.

Genetics & Heredity↗

Methods for Characterizing Fine Particulate Matter Using Satellite Remote-Sensing Data and Ground Observations: Potential Use for Environmental Public Health Surveillance

This study describes and demonstrates different techniques for surfacing daily environmental / hazards data of particulate matter with aerodynamic diameter less than or equal to 2.5 micrometers (PM2.5) for the purpose of integrating respiratory health and environmental data for the Centers for Disease Control and Prevention (CDC s) pilot study of Health and Environment Linked for Information Exchange (HELIX)-Atlanta. It described a methodology for estimating ground-level continuous PM2.5 concentrations using B-Spline and inverse distance weighting (IDW) surfacing techniques and leveraging National Aeronautics and Space Administration (NASA) Moderate Resolution Imaging Spectrometer (MODIS) data to complement The Environmental Protection Agency (EPA) ground observation data. The study used measurements of ambient PM2.5 from the EPA database for the year 2003 as well as PM2.5 estimates derived from NASA s satellite data. Hazard data have been processed to derive the surrogate exposure PM2.5 estimates. The paper has shown that merging MODIS remote sensing data with surface observations of PM2.5 not only provides a more complete daily representation of PM2.5 than either data set alone would allow, but it also reduces the errors in the PM2.5 estimated surfaces. The results of this paper have shown that the daily IDW PM2.5 surfaces had smaller errors, with respect to observations, than those of the B-Spline surfaces in the year studied. However the IDW mean annual composite surface had more numerical artifacts, which could be due to the interpolating nature of the IDW that assumes that the maxima and minima can occur only at the observation points. Finally, the methods discussed in this paper improve temporal and spatial resolutions and establish a foundation for environmental public health linkage and association studies for which determining the concentrations of an environmental hazard such as PM2.5 with good accuracy levels is critical.

Al-Hamdan, Mohammad Z.↗

A History of Collapse Factor Modeling and Empirical Data for Cryogenic Propellant Tanks

One of the major technical problems associated with cryogenic liquid propellant systems used to supply rocket engines and their subassemblies and components is the phenomenon of propellant tank pressurant and ullage gas collapse. This collapse is mainly caused by heat transfer from ullage gas to tank walls and interfacing propellant, which are both at temperatures well below those of this gas. Mass transfer between ullage gas and cryogenic propellant can also occur and have minor to significant secondary effects that can increase or decrease ullage gas collapse. Pressurant gas is supplied into cryogenic propellant tanks in order to initially pressurize these tanks and then maintain required pressures as propellant is expelled from these tanks. The net effect of pressurant and ullage gas collapse is increased total mass and mass flow rate requirements of pressurant gases. For flight vehicles this leads to significant and undesirable weight penalties. For rocket engine component and subassembly ground test facilities this results in significantly increased facility hardware, construction, and operational costs. "Collapse Factor" is a parameter used to quantify the pressurant and ullage gas collapse. Accurate prediction of collapse factors, through analytical methods and modeling tools, and collection and evaluation of collapse factor data has evolved over the years since the start of space exploration programs in the 1950 s. Through the years, numerous documents have been published to preserve results of studies associated with the collapse factor phenomenon. This paper presents a summary and selected details of prior literature that document the aforementioned studies. Additionally other literature that present studies and results of heat and mass transfer processes, related to or providing important insights or analytical methods for the studies of collapse factor, are presented.

deQuay, Laurence↗

A comparison between conventional and LANDSAT based hydrologic modeling: The Four Mile Run case study

Models designed to support the hydrologic studies associated with urban water resources planning require input parameters that are defined in terms of land cover. Estimating the land cover is a difficult and expensive task when drainage areas larger than a few sq. km are involved. Conventional and LANDSAT based methods for estimating the land cover based input parameters required by hydrologic planning models were compared in a case study of the 50.5 sq. km (19.5 sq. mi) Four Mile Run Watershed in Virginia. Results of the study indicate that the LANDSAT based approach is highly cost effective for planning model studies. The conventional approach to define inputs was based on 1:3600 aerial photos, required 110 man-days and a total cost of $14,000. The LANDSAT based approach required 6.9 man-days and cost $2,350. The conventional and LANDSAT based models gave similar results relative to discharges and estimated annual damages expected from no flood control, channelization, and detention storage alternatives.

Ragan, R. M.↗

LOTUS Highlights on Ozone Trend Analyses and Phase 3 Direction

LOTUS (Long-term Ozone Trends and Uncertainties in the Stratosphere) is a SPARC (Stratosphere-troposphere Processes And their Role in Climate)-sponsored effort to foster collaboration between established and early career scientists around the world, with expertise in ozone observations, modeling, and trend tools, with an aim toward innovating new climate research that meets the needs of the ozone trends community and provides vital contributions to the WMO Assessment in an organized and cohesive way. Here we will summarize recent studies associated with the LOTUS effort that perform trend analyses on both total column and vertical profiles of ozone. The main findings of the derived trends from both observations and chemistry climate models have important implications for the status of the ozone layer as they pertain to the efficacy of the Montreal Protocol. These results also present new questions and knowledge gaps that will be outlined as areas of future study in Phase 3 of the LOTUS effort over the next few years to inform the next Assessment.

LOTUS↗

Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions

The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical 𝑂⁡(2) nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature 𝑇 𝑐 = 2.2017⁢(2) with the critical exponent 𝜈 = 0.663⁢(33) for the 3D 𝑂⁡(2) model. In addition, we also study the Berezinskii–Kosterlitz–Thouless (BKT) criticality of the 2D classical 𝑂⁡(2) model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, 𝑇 BKT = 0.8928⁢(2).

lattice field theory↗