Results for “Functional Analysis” — Page 42

DOE OSTI2021

Long-read metagenomics of soil communities reveals phylum-specific secondary metabolite dynamics

Abstract Microbial biosynthetic gene clusters (BGCs) encoding secondary metabolites are thought to impact a plethora of biologically mediated environmental processes, yet their discovery and functional characterization in natural microbiomes remains challenging. Here we describe deep long-read sequencing and assembly of metagenomes from biological soil crusts, a group of soil communities that are rich in BGCs. Taking advantage of the unusually long assemblies produced by this approach, we recovered nearly 3,000 BGCs for analysis, including 712 full-length BGCs. Functional exploration through metatranscriptome analysis of a 3-day wetting experiment uncovered phylum-specific BGC expression upon activation from dormancy, elucidating distinct roles and complex phylogenetic and temporal dynamics in wetting processes. For example, a pronounced increase in BGC transcription occurs at night primarily in cyanobacteria, implicating BGCs in nutrient scavenging roles and niche competition. Taken together, our results demonstrate that long-read metagenomic sequencing combined with metatranscriptomic analysis provides a direct view into the functional dynamics of BGCs in environmental processes and suggests a central role of secondary metabolites in maintaining phylogenetically conserved niches within biocrusts.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

3′ RNA-seq is superior to standard RNA-seq in cases of sparse data but inferior at identifying toxicity pathways in a model organism

The application of RNA-sequencing has led to numerous breakthroughs related to investigating gene expression levels in complex biological systems. Among these are knowledge of how organisms, such as the vertebrate model organism zebrafish (Danio rerio), respond to toxicant exposure. Recently, the development of 3' RNA-seq has allowed for the determination of gene expression levels with a fraction of the required reads compared to standard RNA-seq. While 3' RNA-seq has many advantages, a comparison to standard RNA-seq has not been performed in the context of whole organism toxicity and sparse data. Here, we examined samples from zebrafish exposed to perfluorobutane sulfonamide (FBSA) with either 3' or standard RNA-seq to determine the advantages of each with regards to the identification of functionally enriched pathways. We found that 3' and standard RNA-seq showed specific advantages when focusing on annotated or unannotated regions of the genome. We also found that standard RNA-seq identified more differentially expressed genes (DEGs), but that this advantage disappeared under conditions of sparse data. We also found that standard RNA-seq had a significant advantage in identifying functionally enriched pathways via analysis of DEG lists but that this advantage was minimal when identifying pathways via gene set enrichment analysis of all genes. These results show that each approach has experimental conditions where they may be advantageous. Our observations can help guide others in the choice of 3' RNA-seq vs standard RNA sequencing to query gene expression levels in a range of biological systems.

3’ RNA-seq↗

DOE OSTI2022

ORNL Progress Report on Microreactor Functional Containment Economics

A summary of Oak Ridge National Laboratory’s (ORNL’s) initial contributions to the economic and functional containment evaluation approach for microreactors is presented. A final report will be completed at the end of 2022. This initial progress report does not represent a final product or an expression of a complete technical analysis. Initial contributions from ORNL can be categorized into two parts: (1) description of functional containment as a design optimization tool, and (2) summary of high level technology concepts for an evaluation of economic and functional containment analysis. Additionally, the initial portion of a functional containment evaluation is presented for a generic high temperature gas reactor technology. Remaining tasks include completing the functional containment evaluation by connecting economic and consequence metrics, as well as performing the same effort for other select reactor technologies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

OzMALDI: A Gas-Phase, In-Source Ozonolysis Reaction for Efficient Double-Bond Assignment in Mass Spectrometry Imaging with Matrix-Assisted Laser Desorption/Ionization

Lipids make up an important class of biomolecules with diverse structures and varied chemical functions. This diversity is a major challenge in chemical analysis and limits our understanding of biological functions and regulation. A major way lipid isomers differ is by double-bond (db) position, and analyzing db-isomers is especially challenging for mass spectrometry imaging (MSI). Ozonolysis can be used to determine the dbposition and has been paired with MSI before. However, previous techniques require increased analysis time to allow for gas-phase reactions within an ion trap or ion mobility cell or additional sample preparation time to allow for offline ozonation. Here, we introduce a new ozonolysis method inside the matrix-assisted laser desorption-ionization (MALDI) source, termed OzMALDI, that simultaneously produces ozonides from all unsaturated lipids. This allows us to determine db-positions without adding additional reaction time while maintaining the high mass resolution provided by Orbitrap MS. This new technique is especially effective at determining multiple db-positions in lipids containing polyunsaturated fatty acids, which is a limitation of many previous techniques. OzMALDI-MSI was applied to the analysis of rat brain and genetically engineered Camelina and soybean seed samples, demonstrating the utility of this method and uncovering novel biological information.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Combining GWAS and population genomic analyses to characterize coevolution in a legume‐rhizobia symbiosis

Abstract The mutualism between legumes and rhizobia is clearly the product of past coevolution. However, the nature of ongoing evolution between these partners is less clear. To characterize the nature of recent coevolution between legumes and rhizobia, we used population genomic analysis to characterize selection on functionally annotated symbiosis genes as well as on symbiosis gene candidates identified through a two‐species association analysis. For the association analysis, we inoculated each of 202 accessions of the legume host Medicago truncatula with a community of 88 Sinorhizobia (Ensifer) meliloti strains. Multistrain inoculation, which better reflects the ecological reality of rhizobial selection in nature than single‐strain inoculation, allows strains to compete for nodulation opportunities and host resources and for hosts to preferentially form nodules and provide resources to some strains. We found extensive host by symbiont, that is, genotype‐by‐genotype, effects on rhizobial fitness and some annotated rhizobial genes bear signatures of recent positive selection. However, neither genes responsible for this variation nor annotated host symbiosis genes are enriched for signatures of either positive or balancing selection. This result suggests that stabilizing selection dominates selection acting on symbiotic traits and that variation in these traits is under mutation‐selection balance. Consistent with the lack of positive selection acting on host genes, we found that among‐host variation in growth was similar whether plants were grown with rhizobia or N‐fertilizer, suggesting that the symbiosis may not be a major driver of variation in plant growth in multistrain contexts.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

PET-FBA: A lightweight enzyme allocation and thermodynamics-constrained flux analysis approach to explore Escherichia coli metabolic adaptation to intracellular acidification

Escherichia coli employs diverse strategies to adapt to acidic environments that disrupt enzyme activity and the thermodynamic feasibility of essential reactions. To understand the impact of pH stress on cell metabolism, we present the PET-FBA (pH-, Enzyme protein allocation-, and Thermodynamics-constrained Flux Balance Analysis) framework. PET-FBA extends genome-scale modeling by integrating enzyme protein costs and reaction Gibbs free energy changes. Additionally, by incorporating pH-dependent enzyme kinetics in response to intracellular acidification, this framework enables the simulation of E. coli's metabolic adjustments across varying external pH levels. The model's accuracy is validated by comparing in silico growth simulations with experimental measurements under both anaerobic and aerobic conditions, as well as in silico gene knockouts of essential genes. By explicitly incorporating pH effects, our model accurately replicates the metabolic shift towards lactate production as the primary fermentation product at low pH in anaerobic conditions. This shift is only predicted when enzyme kinetics are dynamically adjusted as a function of pH. Further analysis revealed that this shift can be attributed to the reduced protein efficiency of the acetyl-CoA branch compared to lactate dehydrogenase under acidic stress, which then becomes crucial for maintaining NAD regeneration and cell growth at low pH. Furthermore, we identified strategies for enhancing cell growth under acidic anaerobic conditions by improving the enzyme activity of lactate dehydrogenase and pyruvate formate lyase, which increases NAD production efficiency and reduces enzyme protein allocation costs. Designed as a lightweight yet versatile framework, PET-FBA enables efficient genome-scale metabolic analysis. Using E. coli as a model system, our framework provides a systematic approach to understanding metabolic responses to environmental stress, pinpointing key metabolic bottlenecks, and identifying potential targets for strain optimization.

42 ENGINEERING↗

DOE OSTI2024

Metaanalysis of liana and tree functional traits

The objectives of this project were (i) to determine how tropical trees and lianas differed in terms of their functional traits, and (ii) to parameterize a computational model of tree-liana competition. We carried out a meta-analysis of tree and liana functional traits in order to achieve these goals. First, we downloaded functional trait data from the TRY database during November and December 2019. Traits of interest included leaf, wood, and root functional traits. We included only angiosperm tree and liana species that are found in tropical biomes. We then computed the species average for each trait. The results are included in “TRY_traits_metaanalysis.csv”. We also conducted a second meta-analysis focused on the hydraulic traits of tropical trees and lianas. We used Google Scholar and Web of Science to identify papers that contained hydraulic trait values. The papers that we found were all published between 1997-2019. As with our TRY-based meta-analysis, we included only angiosperm tree and liana species that are found in the tropics, and we computed species averages. The results are contained in the file “hydraulic_traits_metaanalysis.csv”. Both files are in csv format, so they can be read with any plain text editor, as well as programs like R or Excel.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Density functional theory of water with the machine-learned DM21 functional

The delicate interplay between functional-driven and density-driven errors in density functional theory (DFT) has hindered traditional density functional approximations (DFAs) from providing an accurate description of water for over 30 years. Recently, the deep-learned DeepMind 21 (DM21) functional has been shown to overcome the limitations of traditional DFAs as it is free of delocalization error. To determine if DM21 can enable a molecular-level description of the physical properties of aqueous systems within Kohn–Sham DFT, we assess the accuracy of the DM21 functional for neutral, protonated, and deprotonated water clusters. Furthermore, we find that the ability of DM21 to accurately predict the energetics of aqueous clusters varies significantly with cluster size. Additionally, we introduce the many-body MB-DM21 potential derived from DM21 data within the many-body expansion of the energy and use it in simulations of liquid water as a function of temperature at ambient pressure. We find that size-dependent functional-driven errors identified in the analysis of the energetics of small clusters calculated with the DM21 functional result in the MB-DM21 potential systematically overestimating the hydrogen-bond strength and, consequently, predicting a more ice-like local structure of water at room temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

ARCADE Analysis Methods & Validation Pathway

The Advanced Reactor Cyber Analysis and Development Environment (ARCADE) provides an automated analysis system which supports risk-informed performance based (RIPB) evaluations of nuclear control systems. Every possible cyber threat which could lead to consequence is identified by simulating the unsafe control action sequences which transform digital harm into physical harm. Eliminating the simulation of complex digital cyber attack chains cuts out unnecessary computational overhead and focuses directly on the physics of cyber-physical attacks. This focus enables designers to make informed decisions which can entirely eliminate categories of cyber threats against advanced reactors through the physical nature of the plant design. This narrowing of cyber threat against nuclear power plants through the physics of the system is intended to make any remaining threat management and cost efficient. This is the goal of the Tiered Cyber Analysis (TCA) outlined in NRC Draft Regulation Guide (RG) 5.96, which provides a RIPB cybersecurity approach for new reactors. ARCADE has been custom developed to meet the demands of the rigorous analysis required in Tier 1 of the TCA, which forms the foundation of the TCA process. Currently, ARCADE is still under development, but has made significant leaps in capability. A pilot analysis on the opensource Asherah simulator was performed which demonstrated key functionality goals. The next stage of ARCADE development involves improvements to the applications which support the analysis system, and enabling the analysis system to utilize the full suite of unsafe control action simulations. Since the analysis method’s core functions are complete, validation of the analysis method will be started concurrent to the next development stages. The automated analysis ARCADE will provide can radically change the cybersecurity design process for advanced reactors, reducing the cost of security implementation while enhancing cyber resilience. The pathway for ARCADE’s development to this goal has become much clearer. The majority of technical hurdles have been cleared, and the remaining development needs have been solidified. ARCADE is now capable of assisting the advanced reactor design process and directly support advanced reactor industry RIPB practices.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Multiscale spatial analysis of fracture nodes in two dimensions

Spatial arrangement of fractures as a function of scale is an important component of fracture quantification for inferential and predictive modeling. Available methods that analyze fracture spatial arrangement are based on one-dimensional spacing data; therefore, they are limited to semi-parallel fractures. Such methods cannot be applied to fracture networks in higher dimensions, particularly when fractures have different orientations. Here to characterize fracture arrangements in two dimensions, we propose using Ripley’s K-function, as a method of point pattern analysis, to quantify spatial arrangement of fracture nodes. Fracture nodes, such as barycenters, intersection points, and tips, are point-based representations of fracture locations and connectivity within the fracture network. We introduce formulations for isotropic as well as directional analyses of spatial arrangement. In addition, we derive formulations for edge correction in circular and rectangular study domains. Finally, we demonstrate applications of Ripley’s K-function on two natural fracture datasets. Our proposed method supports quantification and characterization of fracture spatial arrangements that allow practitioners to build representative models of fractures in the subsurface.

02 PETROLEUM↗

DOE OSTI2022

Electronic and topological properties of the van der Waals layered superconductor PtTe

We report the crystal growth and structural and electronic properties of superconducting, van der Waals layered PtTe. Easily cleavable crystals with a platelike morphology consistent with the layered structure were grown from a platinum-rich flux. A consistent determination of T c = 0.57 K is made from the onset of diamagnetism, the zero of resistivity, and the midpoint of the heat-capacity jump. The observed behavior is consistent with type-II superconductivity, with upper critical field at T = 0 estimated using the Werthamer-Helfand-Hohenberg theory to be 143 and 65 Oe for fields out of and in the plane, respectively. The heat-capacity discontinuity is close to the weak-coupling BCS value. Density-functional theory calculations and analysis of the electronic structure finds that PtTe is a topological semimetal with numerous surface states but suggests that the superconducting state itself may be topologically trivial. Additionally, angle-resolved photoemission spectroscopy reveals a normal-state Fermi surface in remarkable agreement with theory and confirms the overall topological nature of the material by experimental identification of the surface bands. Together, these findings identify PtTe as an interesting example of a cleavable, topological, and superconducting material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Towards a Circular Economy for PET Bottles in the US

The United States generates the most plastic waste of any country. Along with that GHG emissions from the global plastic economy are expected to increase to 15% of the global carbon budget by 2050. It is imperative that plastic recycling is made a reality to reduce both plastic pollution in the environment and GHG emissions. A portfolio of end-of-life strategies must be implemented to minimize environmental impacts and retain valuable plastic material, but it is challenging to compare options that generate products with different utility and lifetime. Plastic use reduction, reuse and recycling are thus increasingly important, but making informed policy and research decisions within this space can be challenging given the diverse range of available solutions. The novel analysis framework, Plastic Parallel Pathways Platform (4P) has been equipped with consequential life cycle assessment, techno-economic analysis, and a plastic circularity indicator to estimate the greenhouse gas (GHG) emissions, circularity, and cost of polyethylene terephthalate (PET) down-cycling to lower-quality resin, closed-loop recycling to food-grade PET bottles, up-cycling to fiber-reinforced plastic (FRP), and conversion to non-plastic products (electricity, oil) on a United States economy-wide basis. Integrating system dynamics into this robust plastics model that already incorporates techno-economics, circularity, and environmental impacts will enable identification of key bottlenecks between manufacturers, waste sorters, and reclaimers that currently prevent rapid decarbonization of the plastics economy. System dynamics (SD) explore the evolution of activities and technologies based on changed macro parameters such as plastic demand and supply, market shifts, and cross-sectoral interactions. This project particularly aims to explore the interplay between, waste collection, plastic waste sorting, recycling, and manufacturing, as well as the effect of plastic bale quality and plastic reuse initiatives on the surrounding process stages. This functionality will facilitate combinatory analysis in which a portfolio of end-of-life pathways are assessed simultaneously, with the exact makeup of that portfolio affected by parameters such as technology scales, resource constraints, and waste mitigation efforts. Integrating SD with the 4P framework enables analyzing the effect of increased revenue and reinvestment into improving process efficiencies, sorting and collection quantities. Through that, market effects of increased recycled resin availability can be studied for the plastics systems model for the US. The results will help identify technical or economic bottlenecks that currently limit efforts to decarbonize the U.S. plastics economy.

circular economy↗

DOE OSTI2024

Towards a Circular Economy for PET Bottles in the U.S. - 4P Model

The United States generates the most plastic waste of any country. Along with that GHG emissions from the global plastic economy are expected to increase to 15% of the global carbon budget by 2050. It is imperative that plastic recycling is made a reality to reduce both plastic pollution in the environment and GHG emissions. A portfolio of end-of-life strategies must be implemented to minimize environmental impacts and retain valuable plastic material, but it is challenging to compare options that generate products with different utility and lifetime. Plastic use reduction, reuse and recycling are thus increasingly important, but making informed policy and research decisions within this space can be challenging given the diverse range of available solutions. The novel analysis framework, Plastic Parallel Pathways Platform (4P) has been equipped with consequential life cycle assessment, techno-economic analysis, and a plastic circularity indicator to estimate the greenhouse gas (GHG) emissions, circularity, and cost of polyethylene terephthalate (PET) down-cycling to lower-quality resin, closed-loop recycling to food-grade PET bottles, up-cycling to fiber-reinforced plastic (FRP), and conversion to non-plastic products (electricity, oil) on a United States economy-wide basis. Integrating system dynamics into this robust plastics model that already incorporates techno-economics, circularity, and environmental impacts will enable identification of key bottlenecks between manufacturers, waste sorters, and reclaimers that currently prevent rapid decarbonization of the plastics economy. System dynamics (SD) explore the evolution of activities and technologies based on changed macro parameters such as plastic demand and supply, market shifts, and cross-sectoral interactions. This project particularly aims to explore the interplay between, waste collection, plastic waste sorting, recycling, and manufacturing, as well as the effect of plastic bale quality and plastic reuse initiatives on the surrounding process stages. This functionality will facilitate combinatory analysis in which a portfolio of end-of-life pathways are assessed simultaneously, with the exact makeup of that portfolio affected by parameters such as technology scales, resource constraints, and waste mitigation efforts. Integrating SD with the 4P framework enables analyzing the effect of increased revenue and reinvestment into improving process efficiencies, sorting and collection quantities. Through that, market effects of increased recycled resin availability can be studied for the plastics systems model for the US. The results will help identify technical or economic bottlenecks that currently limit efforts to decarbonize the U.S. plastics economy.

carbon↗

DOE OSTI2024

Towards a Circular Economy for PET Bottles in the U.S. - 4P Framework

The United States generates the most plastic waste of any country. Along with that GHG emissions from the global plastic economy are expected to increase to 15% of the global carbon budget by 2050. It is imperative that plastic recycling is made a reality to reduce both plastic pollution in the environment and GHG emissions. A portfolio of end-of-life strategies must be implemented to minimize environmental impacts and retain valuable plastic material, but it is challenging to compare options that generate products with different utility and lifetime. Plastic use reduction, reuse and recycling are thus increasingly important, but making informed policy and research decisions within this space can be challenging given the diverse range of available solutions. The novel analysis framework, Plastic Parallel Pathways Platform (4P) has been equipped with consequential life cycle assessment, techno-economic analysis, and a plastic circularity indicator to estimate the greenhouse gas (GHG) emissions, circularity, and cost of polyethylene terephthalate (PET) down-cycling to lower-quality resin, closed-loop recycling to food-grade PET bottles, up-cycling to fiber-reinforced plastic (FRP), and conversion to non-plastic products (electricity, oil) on a United States economy-wide basis. Integrating system dynamics into this robust plastics model that already incorporates techno-economics, circularity, and environmental impacts will enable identification of key bottlenecks between manufacturers, waste sorters, and reclaimers that currently prevent rapid decarbonization of the plastics economy. System dynamics (SD) explore the evolution of activities and technologies based on changed macro parameters such as plastic demand and supply, market shifts, and cross-sectoral interactions. This project particularly aims to explore the interplay between, waste collection, plastic waste sorting, recycling, and manufacturing, as well as the effect of plastic bale quality and plastic reuse initiatives on the surrounding process stages. This functionality will facilitate combinatory analysis in which a portfolio of end-of-life pathways are assessed simultaneously, with the exact makeup of that portfolio affected by parameters such as technology scales, resource constraints, and waste mitigation efforts. Integrating SD with the 4P framework enables analyzing the effect of increased revenue and reinvestment into improving process efficiencies, sorting and collection quantities. Through that, market effects of increased recycled resin availability can be studied for the plastics systems model for the US. The results will help identify technical or economic bottlenecks that currently limit efforts to decarbonize the U.S. plastics economy.

circular economy↗

DOE OSTI2024

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Scalar modular bootstrap and zeros of the Riemann zeta function

Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with U(1) c symmetry. From this crossing equation, we derive bounds on the scalar gap of all such theories. Rather remarkably, our crossing equation contains information about all nontrivial zeros of the Riemann zeta function. As a result, we rephrase the Riemann hypothesis purely as a statement about the asymptotic density of scalar operators in certain two-dimensional conformal field theories. We discuss generalizations to theories with only Virasoro symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

GADRAS-DRF Enhancements for Safeguards – Custom Peak Fitting to Enhance Model Fitting and Isotopics

One major software update was accomplished within the Gamma Detector Response and Analysis Software-Detector Response Function (GADRAS-DRF) package. This update allows users to adjust individual peak fits for use in subsequent analysis processes within GADRAS-DRF. A graphical user interface (GUI) was implemented so users can see the effect of their fit adjustments on the spectrum. This new feature will enhance the capability of the previously funded auto-enrichment and peak-based 1D model fit feature that was implemented in FY23 (Fiscal Year). Isotopic analysis was performed using M400 data obtained from uranium standards and the isotopic assessment is given with and without manual peak adjustments.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5',10',20',40',80',160',320', and 640', and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80'. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320', but at a low dimensionless threshold ν = –2.5. Under a Gaussian assumption, this would amount to a deviation of ~4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320'. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640', both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.

79 ASTRONOMY AND ASTROPHYSICS↗