Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “factorization”

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

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

At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

ENABLING BUSINESS-DRIVEN INNOVATION THROUGH HUMAN FACTORS ENGINEERING IN NUCLEAR POWER PLANTS

For existing United States nuclear power plant fleet to remain economically viable, the nuclear industry needs to fundamentally change the way in which these plants are operated, maintained, and supported. A digital transformation is a key strategy to address this challenge. Though, guidance in this area is a continued effort. One framework to support innovation in the nuclear industry has taken a broader perspective by focusing on how technology can be used to meet specific business needs and work for the people and processes at hand. This work discusses the role and value of human factors engineering within this nuclear innovation framework. Human factors methods are presented here regarding how they address the phases of nuclear innovation. This work seeks to describe how human factors can be applied in nuclear innovation by strengthening the alignment of technology, people, processes, and regulations such that the needs of the business is addressed.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2017

A structured data model frame for human factors application - 175

Building a Human Factors analysis and Verification and Validation case for new control rooms and even for control room modifications is a highly labor intensive project. Any optimization that can be made in the process translates into savings in the overall control room project schedule and budget. Several support tools from word, to excel, mind maps and databases have been traditionally used by human factors practitioners to conduct the analysis and document its results. While the use of these tools has had satisfactory results, they don't provide in our experience strong enough means for configuration control management, to avoid duplicities, streamline the analysis processes and allow collaborative team efforts. This paper documents how the established practices (methods, processes and tools) were questioned, which were the sources for comparison and how the results were translated into requirements for the new tool constituting the data frame model for Human Factors Engineering applications. The exercise has allowed us to evaluate the efficiency of our current practices in comparison to previous ones while improving our compliance with the quality assurance standards. (authors)

42 ENGINEERING↗
DOE OSTI2017

Human factors engineering process to support human-system interface design in control room modernization - 351

The primary objective of the United States (U.S.) Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) program is to sustain operation of the existing commercial nuclear power plants (NPPs) through a multi-pathway approach in conducting research and development (R and D). The Advanced Instrumentation, Information, and Control (II and C) System Technologies pathway conducts targeted R and D to address aging and reliability concerns with legacy instrumentation and control (I and C) and other information systems in existing U.S. NPPs. Control room modernization is an important part following this pathway, and human factors experts at Idaho National Laboratory (INL) have been involved in conducting R and D to support migration of new digital main control room (MCR) technologies from legacy analog and legacy digital I and C. This paper describes a human factors engineering (HFE) process that supports human-system interface (HSI) design in MCR modernization activities, particularly with migration of old digital to new digital I and C. The process described in this work is an expansion from the LWRS Report INL/EXT-16-38576, and is a requirements-driven approach that aligns with NUREG-0711 requirements. The work described builds upon the existing literature by adding more detail around key tasks and decisions to make when transitioning from HSI Design into Verification and Validation (V and V). The overall objective of this process is to inform HSI design and elicit specific, measurable, and achievable human factors criteria for new digital technologies. Upon following this process, utilities should have greater confidence with transitioning from HSI design into V and V. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

General-Purpose Unsupervised Cyber Anomaly Detection via Non-Negative Tensor Factorization

Distinguishing malicious anomalous activities from unusual but benign activities is a fundamental challenge for cyber defenders. Prior studies have shown that statistical user behavior analysis yields accurate detections by learning behavior profiles from observed user activity. These unsupervised models are able to generalize to unseen types of attacks by detecting deviations from normal behavior, without knowledge of specific attack signatures. However, approaches proposed to date based on probabilistic matrix factorization are limited by the information conveyed in a two-dimensional space. Non-negative tensor factorization, on the other hand, is a powerful unsupervised machine learning method that naturally models multi-dimensional data, capturing complex and multi-faceted details of behavior profiles. Herein, our new unsupervised statistical anomaly detection methodology matches or surpasses state-of-the-art supervised learning baselines across several challenging and diverse cyber application areas, including detection of compromised user credentials, botnets, spam e-mails, and fraudulent credit card transactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Machine Learning to Identify Geologic Factors Associated with Production in Geothermal Fields: A Case-Study Using 3D Geologic Data from Brady Geothermal Field and NMFk

In this paper, we present an analysis using unsupervised machine learning (ML) to identify the key geologic factors that contribute to the geothermal production in Brady geothermal field. Brady is a hydrothermal system in northwestern Nevada that supports both electricity production and direct use of hydrothermal fluids. Transmissive fuid-fow pathways are relatively rare in the subsurface, but are critical components of hydrothermal systems like Brady and many other types of fuid-fow systems in fractured rock. Here, we analyze geologic data with ML methods to unravel the local geologic controls on these pathways. The ML method, non-negative matrix factorization with k-means clustering (NMFk), is applied to a library of 14 3D geologic characteristics hypothesized to control hydrothermal circulation in the Brady geothermal field. Our results indicate that macro-scale faults and a local step-over in the fault system preferentially occur along production wells when compared to injection wells and non-productive wells. We infer that these are the key geologic characteristics that control the through-going hydrothermal transmission pathways at Brady. Our results demonstrate: (1) the specific geologic controls on the Brady hydrothermal system and (2) the efficacy of pairing ML techniques with 3D geologic characterization to enhance the understanding of subsurface processes. This submission includes the published journal article detailing this work, the published 3D geologic map of the Brady Geothermal Area used as a basis to develop structural and geological variables that are hypothesized to control or effect permeability or connectivity, 3D well data, along which geologic data were sampled for PCA analyses, and associated metadata file. This work was done using the GeoThermalCloud framework, which is part of SmartTensors (both are linked below).

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

Reproductive Factors and Endometrial Cancer Risk Among Women

Despite evidence of an association between reproductive factors and endometrial cancer risk, prospective studies have been conducted mainly in non-Asian countries. To assess the association between reproductive factors, such as number of deliveries, age at menarche, or menopause, and endometrial cancer risk. This cohort study used pooled individual data from 13 prospective cohort studies conducted between 1963 and 2014 in the Asia Cohort Consortium. Participants were Asian women. Data analysis was conducted from September 2019 to April 2023. Reproductive factors were assessed using a questionnaire in each cohort. The main outcome was time to incidence of endometrial cancer. A Cox proportional hazards model was used to calculate hazard ratios (HRs) and 95% CIs.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Toward Ultra‐High‐Quality‐Factor Wireless Masing Magnetic Resonance Sensing

It has recently been shown that a bolus of hyperpolarized nuclear spins can yield stimulated emission signals similar in nature to maser signals, potentially enabling new ways of sensing hyperpolarized contrast media, including most notably [1- 13 C]pyruvate that is under evaluation in over 50 clinical trials for metabolic imaging of cancer. The stimulated NMR signal emissions lasting for minutes do not require radio-frequency excitation, offering unprecedented advantages compared to conventional MR sensing. However, creating nuclear spin maser emission is challenging in practice due to stringent fundamental requirements, making practical in vivo applications hardly possible using conventional passive MR detectors. Here, in this study, we demonstrate the utility of a wireless NMR maser detector, the quality factor of which was enhanced 22-fold (to 1,670) via parametric pumping. This active-feedback technique breaks the intrinsic fundamental limit of NMR detector circuit quality factor. We show the use of parametric pumping to reduce the threshold requirement for inducing nuclear spin masing at 300 MHz resonance frequency in a preclinical MRI scanner. Indeed, stimulated emission from hyperpolarized protons was obtained under highly unfavorable conditions of low magnetic field homogeneity (T 2 * of 3 ms). Greater gains of the quality factor of the MR detector (up to 1 million) were also demonstrated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Association of female reproductive and hormonal factors with gallbladder cancer risk in Asia: A pooled analysis of the Asia Cohort Consortium

Abstract The female predominance of gallbladder cancer (GBC) has led to a hypothesis regarding the hormone‐related aetiology of GBC. We aimed to investigate the association between female reproductive factors and GBC risk, considering birth cohorts of Asian women. We conducted a pooled analysis of 331,323 women from 12 cohorts across 4 countries (China, Japan, Korea, and Singapore) in the Asia Cohort Consortium. Cox proportional hazard models were used to estimate the hazard ratios (HRs) and corresponding 95% confidence intervals (CIs) to assess the association between reproductive factors (age at menarche, parity, age at first delivery, breastfeeding, and age at menopause) and GBC risk. We observed that a later age at menarche was associated with an increased risk of GBC (HR 1.4, 95% CI 1.16–1.70 for 17 years and older vs. 13–14 years), especially among the cohort born in 1940 and later (HR 2.5, 95% CI 1.50–4.35). Among the cohort born before 1940, women with a later age at first delivery showed an increased risk of GBC (HR 1.56, 95% CI 1.08–2.24 for 31 years of age and older vs. 20 years of age and younger). Other reproductive factors did not show a clear association with GBC risk. Later ages at menarche and at first delivery were associated with a higher risk of GBC, and these associations varied by birth cohort.

Shin, Aesun↗
DOE OSTI2017

Production of Macrophage Inhibitory Factor (MIF) by Primary Sertoli Cells; Its Possible Involvement in Migration of Spermatogonial Cells

Macrophage migration inhibitory factor (MIF) is a multifunctional molecule. MIF was originally identified as a T‐cell‐derived factor responsible for the inhibition of macrophage migration. In testicular tissue of adult rats, MIF is constitutively expressed by Leydig cells under physiological conditions. The aim of this study was to examine MIF levels in testicular homogenates from different aged mice, and the capacity of Sertoli cells to produce it. We also examined MIF involvement in spermatogonial cell migration. Similar levels of MIF protein were detected in testicular homogenates of mice of different ages (1–8‐week‐old). However, the RNA expression levels of MIF were high in 1‐week‐old mice and significantly decreased with age compared to 1‐week‐old mice. MIF was stained in Sertoli, Leydig cells, and developed germ cells in the seminiferous tubules. Isolated Sertoli cells from 1‐week‐old mice stained to MIF. Cultures of Sertoli cells from 1‐week‐old mice produced and expressed high levels of MIF which significantly decreased with age. MIF was localized in the cytoplasm and nucleus of Sertoli cell cultures isolated from 1‐week‐old mice; however, it was localized only in the cytoplasm and branches of cultures isolated from 8‐week‐old mice. MIFR was detected in GFRα1 and Sertoli cells. MIF could induce migration of spermatogonial cells, and this effect was synergistic with glial cell‐line neurotrophic factor. Our results show, for the first time, the capacity of Sertoli cells to produce MIF under normal conditions and that MIFR expressed in GFRα1 and Sertoli cells. We also showed that MIF induced spermatogonial cell migration. J. Cell. Physiol. 232: 2869–2877, 2017. © 2016 Wiley Periodicals, Inc.

Huleihel, Mahmoud↗
DOE OSTI2014

Patient-based radiographic exposure factor selection: a systematic review

Digital technology has wider exposure latitude and post-processing algorithms which can mask the evidence of underexposure and overexposure. Underexposure produces noisy, grainy images which can impede diagnosis and overexposure results in a greater radiation dose to the patient. These exposure errors can result from inaccurate adjustment of exposure factors in response to changes in patient thickness. This study aims to identify all published radiographic exposure adaptation systems which have been, or are being, used in general radiography and discuss their applicability to digital systems. Studies in EMBASE, MEDLINE, CINAHL and SCOPUS were systematically reviewed. Some of the search terms used were exposure adaptation, exposure selection, exposure technique, 25% rule, 15% rule, DuPont™ Bit System and radiography. A manual journal-specific search was also conducted in The Radiographer and Radiologic Technology. Studies were included if they demonstrated a system of altering exposure factors to compensate for variations in patients for general radiography. Studies were excluded if they focused on finding optimal exposures for an ‘average’ patient or focused on the relationship between exposure factors and dose. The database search uncovered 11 articles and the journal-specific search uncovered 13 articles discussing systems of exposure adaptation. They can be categorised as simple one-step guidelines, comprehensive charts and computer programs. Only two papers assessed the efficacy of exposure adjustment systems. No literature compares the efficacy of exposure adaptations system for film/screen radiography with digital radiography technology nor is there literature on a digital specific exposure adaptation system.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2022

Factors influencing pregnancy, litter size, and reproductive parameters of invasive wild pigs

Abstract Reproduction is the most energetically expensive life stage with the demands of productivity representing a balance between physiological requirements and environmental conditions. Wild pigs ( Sus scrofa ) throughout most of North America are genetic hybrids of feral domestic pigs and wild boar and have the highest reproductive potential of any wild ungulate. The phenology of reproduction, extent of multiple reproductive events per year, how individual and extrinsic factors contribute to variability in productivity, and impact of genetic lineage on these parameters is not well understood in wild pigs. We quantified reproductive parameters in wild pigs relative to a suite of individual and environmental attributes across seasons and multiple years in South Carolina, USA, from March 2017 and May 2020. We hypothesized that individual attributes (mass, age class, number of teats, rump fat, relative genetic association to wild boar vs. domestic pigs) and extrinsic factors (mast availability) would influence probability of pregnancy and fetal litter size. Wild pigs produced offspring throughout all months with peaks in conception corresponding to a seasonal pulse in food availability. The likelihood of pregnancy was influenced by female mass and nutritional condition and was greatest during years with abundant resources. Similarly, litter size increased with female mass and age, implying larger and older females represent the most important group for population recruitment. In evaluating the relationship between reproductive output and ancestral associations to domestic pigs versus wild boar, the proportion of wild boar ancestry was not an important influence on productivity in our population. We determined juveniles reach a physiological threshold of sexual maturity at approximately 30 kg. Average litter size was comparable to other populations, and wild pigs maintain an average fetal litter size of 5.43 offspring despite 13.6% embryonic mortality. A thorough understanding of biotic and extrinsic factors influencing reproduction are important for realistic population models, which are necessary for identifying areas to focus management needs and implementation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

Transcriptome and phenotyping analyses support a role for chloroplast sigma factor 2 in red‐light‐dependent regulation of growth, stress, and photosynthesis

Abstract Sigma factor ( SIG ) proteins contribute to promoter specificity of the plastid‐encoded RNA polymerase during chloroplast genome transcription. All six members of the SIG family, that is, SIG 1– SIG 6, are nuclear‐encoded proteins targeted to chloroplasts. Sigma factor 2 ( SIG 2) is a phytochrome‐regulated protein important for stoichiometric control of the expression of plastid‐ and nuclear‐encoded genes that impact plastid development and plant growth and development. Among SIG factors, SIG 2 is required not only for transcription of chloroplast genes (i.e., anterograde signaling), but also impacts nuclear‐encoded, photosynthesis‐related, and light signaling‐related genes (i.e., retrograde signaling) in response to plastid functional status. Although SIG 2 is involved in photomorphogenesis in Arabidopsis, the molecular bases for its role in light signaling that impacts photomorphogenesis and aspects of photosynthesis have only recently begun to be investigated. Previously, we reported that SIG 2 is necessary for phytochrome‐mediated photomorphogenesis specifically under red (R) and far‐red light, thereby suggesting a link between phytochromes and nuclear‐encoded SIG 2 in light signaling. To explore transcriptional roles of SIG 2 in R‐dependent growth and development, we performed RNA sequencing analysis to compare gene expression in sig2‐2 mutant and Col‐0 wild‐type seedlings at two developmental stages (1‐ and 7‐day). We identified a subset of misregulated genes involved in growth, hormonal cross talk, stress responses, and photosynthesis. To investigate the functional relevance of these gene expression analyses, we performed several comparative phenotyping tests. In these analyses, strong sig2 mutants showed insensitivity to bioactive GA 3 , high intracellular levels of hydrogen peroxide (H 2 O 2 ) indicative of a stress response, and specific defects in photosynthesis, including elevated levels of cyclic electron flow ( CEF ) and nonphotochemical quenching ( NPQ ). We demonstrated that SIG 2 regulates a broader range of physiological responses at the molecular level than previously reported, with specific roles in red‐light‐mediated photomorphogenesis.

Oh, Sookyung↗
DOE OSTI2021

Influence of biotic and abiotic factors on home range size and shape of invasive wild pigs ( Sus scrofa )

Determining factors influencing animal movements at a temporal scale that is similar to that at which management actions are conducted (e.g. weekly) is crucial for identifying efficient methods of wildlife conservation and management. Using global positioning system (GPS) data from 49 wild pigs in the southeast United States, we constructed weekly 50% and 95% utilization distributions to quantify the effects of biotic and abiotic factors on weekly core area and home range size, as well as home range shape. Here we found vegetative composition (i.e. proportion of bottomland hardwoods), season (based on forage availability), meteorological conditions (i.e. temperature and pressure), and sex influenced wild pig weekly home range and core area size, while vegetative composition (i.e. proportion of upland pines) and landscape features (i.e. distance to streams) also were important factors influencing home range shape. At close distances to streams, wild pigs had more elongate home ranges when their home ranges comprised less upland pine habitat; however, farther from streams, there was no change in home range shape across fluctuating proportions of upland pines. These results demonstrate that fine-scale wild pig home ranges and movements are pliable from week to week and influenced by several habitat, landscape, and meteorological attributes that can easily be quantified from available land use and meteorological databases. These findings are important for designing monitoring studies, identifying high risk zones for disease transmission, planning response to disease emergence events, and allowing more effective and efficient short-term management planning.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

A combinatorial approach to synthetic transcription factor-promoter combinations for yeast strain engineering

Despite the need for inducible promoters in strain development efforts, the majority of engineering in Saccharomyces cerevisiae continues to rely on a few constitutively active or inducible promoters. Building on advances that use the modular nature of both transcription factors and promoter regions, we have built a library of hybrid promoters that are regulated by a synthetic transcription factor. The hybrid promoters consist of native S. cerevisiae promoters, in which the operator regions have been replaced with sequences that are recognized by the bacterial LexA DNA binding protein. Correspondingly, the synthetic transcription factor (TF) consists of the DNA binding domain of the LexA protein, fused with the human estrogen binding domain and the viral activator domain, VP16. The resulting system with a bacterial DNA binding domain avoids the transcription of native S. cerevisiae genes, and the hybrid promoters can be induced using estradiol, a compound with no detectable impact on S. cerevisiae physiology. Using combinations of one, two or three operator sequence repeats and a set of native S. cerevisiae promoters, we obtained a series of hybrid promoters that can be induced to different levels, using the same synthetic TF and a given estradiol. Finally, this set of promoters, in combination with our synthetic TF, has the potential to regulate numerous genes or pathways simultaneously, to multiple desired levels, in a single strain.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Multifrontal Non-negative Matrix Factorization

Non-negative matrix factorization (Nmf) is an important tool in high-performance large scale data analytics with applications ranging from community detection, recommender system, feature detection and linear and non-linear unmixing. While traditional Nmf works well when the data set is relatively dense, however, it may not extract sufficient structure when the data is extremely sparse. Specifically, traditional Nmf fails to exploit the structured sparsity of the large and sparse data sets resulting in dense factors. We propose a new algorithm for performing Nmf on sparse data that we call multifrontal Nmf (Mf-Nmf) since it borrows several ideas from the multifrontal method for unconstrained factorization (e.g. LU and QR). We also present an efficient shared memory parallel implementation of Mf-Nmf and discuss its performance and scalability. We conduct several experiments on synthetic and realworld datasets and demonstrate the usefulness of the algorithm by comparing it against standard baselines. We obtain a speedup of 1.2x to 19.5x on 24 cores with an average speed up of 10.3x across all the real world datasets.

Sao, Piyush↗
DOE OSTI2020

Weak neutral current axial form factor using $ \left(\overline{\nu}\right)\nu $-nucleon scattering and lattice QCD inputs

We present a determination of the neutral current weak axial charge $G$ $^{Z}_{A}$(0) = –0.654(3) stat (5) sys using the strange quark axial charge $G$ $^{s}_{A}$(0) calculated with lattice QCD. We then perform a phenomenological analysis, where we combine the strange quark electromagnetic form factor from lattice QCD with (anti)neutrino-nucleon scattering differential cross section from MiniBooNE experiments in a momentum transfer region 0.24 ≲ Q 2 ≲ 0.71 GeV 2 to determine the neutral current weak axial form factor $G$ $^{Z}_{A}$(Q 2 ) in the range of 0 ≲ Q 2 ≤ 1 GeV 2 . This yields a phenomenological value of $G$ $^{Z}_{A}$(0) = –0.687(89)stat(40)sys. The value of $G$ $^{Z}_{A}$(0) constrained by the lattice QCD calculation of $G$ $^{s}_{A}$(0), when compared to its phenomenological determination, provides a significant improvement in precision and accuracy and can be used to provide a constraint on the fit to $G$ $^{Z}_{A}$(Q 2 ) for Q 2 > 0. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near Q 2 = 0 and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $G$ $^{Z}_{A}$(Q 2 ) obtained from the (anti)neutrino-nucleon scattering cross section data requires a nonzero contribution of the strange quark electromagnetic form factor. We demonstrate the robustness of our analysis by providing a post-diction of the BNL E734 experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Charged-particle nuclear modification factors in PbPb and pPb collisions at $ \sqrt{s_{\mathrm{N}\;\mathrm{N}}}=5.02 $ TeV

The spectra of charged particles produced within the pseudorapidity window |η| < 1 at $ \sqrt{s_{\mathrm{N}\,\mathrm{N}}}=5.02 $ TeV are measured using 404 μb$^{−1}$ of PbPb and 27.4 pb$^{−1}$ of pp data collected by the CMS detector at the LHC in 2015. The spectra are presented over the transverse momentum ranges spanning 0.5 < p$_{T}$ < 400 GeV in pp and 0.7 < p$_{T}$ < 400 GeV in PbPb collisions. The corresponding nuclear modification factor, R$_{AA}$, is measured in bins of collision centrality. The R$_{AA}$ in the 5% most central collisions shows a maximal suppression by a factor of 7-8 in the p$_{T}$ region of 6-9 GeV. This dip is followed by an increase, which continues up to the highest p$_{T}$ measured, and approaches unity in the vicinity of p$_{T}$ = 200 GeV. The R$_{AA}$ is compared to theoretical predictions and earlier experimental results at lower collision energies. The newly measured pp spectrum is combined with the pPb spectrum previously published by the CMS collaboration to construct the pPb nuclear modification factor, R$_{pA}$, up to 120 GeV. For p$_{T}$ > 20 GeV, R$_{pA}$ exhibits weak momentum dependence and shows a moderate enhancement above unity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A three-point form factor through five loops

We bootstrap the three-point form factor of the chiral part of the stress­tensor supermultiplet in planar $\mathcal{N}$ = 4 super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known conditions on the first, second, and final entries of the symbol, combined with new multiple-final-entry conditions, “extended-Steinmann-like” conditions, and near-collinear data from the recently-developed form factor operator product expansion. Our results are expected to give the maximally transcendental parts of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD. At two loops, the extended-Steinmann-like space of functions we describe contains all transcendental functions required for four-point amplitudes with one massive and three massless external legs, and all massless internal lines, including processes such as gg → Hg and γ * → $q\overline{q}g$. We expect the extended-Steinmann-like space to contain these amplitudes at higher loops as well, although not to arbitrarily high loop order. We present evidence that the planar $\mathcal{N}$ = 4 three-point form factor can be placed in an even smaller space of functions, with no independent ζ values at weights two and three.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗