In this paper, we show that the diffraction of the primes is absolutely continuous, showing no bright spots (Bragg peaks). We introduce the notion of counting diffraction, extending the classical notion of (density) diffraction to sets of density zero. We develop the counting diffraction theory and give many examples of sets of zero density of all possible spectral types.

In this article, it is shown that the lattice of C$^*$-covers of an operator algebra does not contain enough information to distinguish operator algebras up to completely isometric isomorphism. In addition, four natural equivalences of the lattice of C$^*$-covers are developed and proven to be distinct. The lattice of C$^*$-covers of direct sums and tensor products are studied. Along the way key examples are found of operator algebras, each of which generates exactly n C$^*$-algebras up to $*$-isomorphism, and a simple operator algebra that is not similar to a C$^*$-algebra.

A 350 14C yr discrepancy was found between dates on postcranial remains and mandibular teeth on what was thought to be the same individual from the Early Neolithic cemetery of Shamanka II, Lake Baikal. Stable nitrogen isotope results suggested a major shift in diet between childhood (when the teeth formed) and adulthood (represented by the postcrania), which could have resulted in different 14C ages through a freshwater reservoir effect. Subsequent additional dating on the mandible and postcranial elements, however, indicated that the mandible actually belonged to a different individual. More subtle reservoir effects can be seen on the sequentially forming teeth and mandible. The practice by prehistoric hunter-gatherers of Lake Baikal of re-opening graves and removing cranial elements has long been known, but this is the first evidence for the inclusion of a mandible from a separate individual, though whether it was intentional or incidental is uncertain. As well as providing new insights into mid-Holocene mortuary practices in the region, our findings raise a cautionary note for the examination of disturbed graves.

Knowledge graphs have become a common approach for knowledge representation. Yet, the application of graph methodology is elusive due to the sheer number and complexity of knowledge sources. In addition, semantic incompatibilities hinder efforts to harmonize and integrate across these diverse sources. As part of The Biomedical Translator Consortium, we have developed a knowledge graph–based question-answering system designed to augment human reasoning and accelerate translational scientific discovery: the Translator system. We have applied the Translator system to answer biomedical questions in the context of a broad array of diseases and syndromes, including Fanconi anemia, primary ciliary dyskinesia, multiple sclerosis, and others. A variety of collaborative approaches have been used to research and develop the Translator system. One recent approach involved the establishment of a monthly “Question-of-the-Month (QotM) Challenge” series. Herein, we describe the structure of the QotM Challenge; the six challenges that have been conducted to date on drug-induced liver injury, cannabidiol toxicity, coronavirus infection, diabetes, psoriatic arthritis, and ATP1A3-related phenotypes; the scientific insights that have been gleaned during the challenges; and the technical issues that were identified over the course of the challenges and that can now be addressed to foster further development of the prototype Translator system. We close with a discussion on Large Language Models such as ChatGPT and highlight differences between those models and the Translator system.

The IntCal family of radiocarbon (14C) calibration curves is based on research spanning more than three decades. The IntCal group have collated the 14C and calendar age data (mostly derived from primary publications with other types of data and meta-data) and, since 2010, made them available for other sorts of analysis through an open-access database. This has ensured transparency in terms of the data used in the construction of the ratified calibration curves. As the IntCal database expands, work is underway to facilitate best practice for new data submissions, make more of the associated metadata available in a structured form, and help those wishing to process the data with programming languages such as R, Python, and MATLAB. The data and metadata are complex because of the range of different types of archives. A restructured interface, based on the “IntChron” open-access data model, includes tools which allow the data to be plotted and compared without the need for export. The intention is to include complementary information which can be used alongside the main 14C series to provide new insights into the global carbon cycle, as well as facilitating access to the data for other research applications. Overall, this work aims to streamline the generation of new calibration curves.

Temporal and spatial variation in radiocarbon (14C) in the atmosphere has been the subject of investigation from the first pioneering work of Libby and Arnold. However, as the precision of measurements has improved, now by almost two orders of magnitude, what constitutes a significant variation has also changed. Furthermore, it has become possible to test degrees of variation over much longer timescales and with ever wider geographic coverage. As knowledge has improved, the interpretation of 14C measurements has had to be revised. These re-evaluations, and the loss of chronological precision that comes with accurate calibration, have often been seen as an unfortunate drawback in the 14C dating method. However, these problems have stimulated extensive research in global 14C records, statistical methods for dealing with complex 14C data, and measurement methods. This research has provided a wealth of information useful for other scientific challenges, most notably the quantification of the global carbon cycle, but also enabled, in the right circumstances, measurement precision an order of magnitude better than if there had been no variation in atmospheric 14C. Challenges remain but the research undertaken for 14C calibration has, through its ingenuity and innovation, provided rich scientific dividends in both chronology and broader geoscience.

Prehistoric shell mounds can be useful for the quantification of the radiocarbon marine reservoir effect (MRE) and, at the same time, knowledge about the MRE allows for the establishment of robust chronologies for these sites. This creates a loop in which the archaeological setting has a dual role: it is part of both the method and the application. Therefore, it is paramount to address these sites from both archaeological and environmental perspectives, investigating their origin and diagenesis in order to overcome biases caused by post-depositional alterations. In this study, samples of bone, charcoal and shell from a Late Holocene shell mound in Southern Brazil, the Sambaqui de Cabeçuda, were analyzed following a multidisciplinary approach to disentangle the complex relationships between archaeology and the environment. We performed X-ray diffraction, radiocarbon dating, stable isotopes (δ13C, δ18O, δ15N) and anthracology analyses as well as Bayesian Chronological Models and Isotope Mixing Models to assess the local MRE and to reconstruct the diet of Cabeçuda builders. Our results reveal a negative local correction for the MRE (ΔR = –263 ± 46 14C yr), expected for the lagoon next to the site, and diets with considerable intakes of marine proteins. We examine the implications of these results for the chronology of the site and discuss a series of complications when performing MRE studies using shell mound sites.

We resolve the isomorphism problem for tensor algebras of unital multivariable dynamical systems. Specifically, we show that unitary equivalence after a conjugation for multivariable dynamical systems is a complete invariant for complete isometric isomorphisms between their tensor algebras. In particular, this settles a conjecture of Davidson and Kakariadis, Inter. Math. Res. Not. 2014 (2014), 1289–1311 relating to work of Arveson, Acta Math. 118 (1967), 95–109 from the 1960s, and extends related work of Kakariadis and Katsoulis, J. Noncommut. Geom. 8 (2014), 771–787.

The Glastonbury Lake Village in Somerset, UK, is made up of 90 mounds comprising 40 roundhouses. Excavations between 1892 and 1907 revealed Iron Age structural and material remains unparalleled in Western Europe. The settlement's exact chronology, however, has remained uncertain. Here, the authors present a programme of radiocarbon and dendrochronological dating and chronological modelling on samples from recent excavations. The results indicate that the site was founded in the early second century cal BC, with the last structures being built just over a century later. This new, robust chronology can be used to date a wide range of associated material culture, and complements chronologies established for other Iron Age sites.

Radiocarbon dating and Bayesian chronological modelling have provided precise new dating for the henge monument of Mount Pleasant in Dorset, excavated in 1970–1. A total of 59 radiocarbon dates are now available for the site and modelling of these has provided a revised sequence for the henge enclosure and its various constituent parts: the timber palisaded enclosure, the Conquer Barrow, and the ditch surrounding Site IV, a concentric timber and stone monument. This suggests that the henge was probably built in the 26th century cal bc, shortly followed by the timber palisade and Site IV ditch. These major construction events took place in the late Neolithic over a relatively short timespan, probably lasting 35–125 years. The principal results are discussed for each element of the site, including comparison with similar monument types elsewhere in Britain and Ireland, and wider implications for late Neolithic connections and later activity at the site associated with Beaker pottery are explored.

To create a reliable radiocarbon calibration curve, one needs not only high-quality data but also a robust statistical methodology. The unique aspects of much of the calibration data provide considerable modeling challenges and require a made-to-measure approach to curve construction that accurately represents and adapts to these individualities, bringing the data together into a single curve. For IntCal20, the statistical methodology has undergone a complete redesign, from the random walk used in IntCal04, IntCal09 and IntCal13, to an approach based upon Bayesian splines with errors-in-variables. The new spline approach is still fitted using Markov Chain Monte Carlo (MCMC) but offers considerable advantages over the previous random walk, including faster and more reliable curve construction together with greatly increased flexibility and detail in modeling choices. This paper describes the new methodology together with the tailored modifications required to integrate the various datasets. For an end-user, the key changes include the recognition and estimation of potential over-dispersion in 14C determinations, and its consequences on calibration which we address through the provision of predictive intervals on the curve; improvements to the modeling of rapid 14C excursions and reservoir ages/dead carbon fractions; and modifications made to, hopefully, ensure better mixing of the MCMC which consequently increase confidence in the estimated curve.

The Khao Wong Prachan Valley of central Thailand is one of four known prehistoric loci of copper mining, smelting and casting in Southeast Asia. Many radiocarbon determinations from bronze-consumption sites in north-east Thailand date the earliest copper-base metallurgy there in the late second millennium BC. By applying kernel density estimation analysis to approximately 100 new AMS radiocarbon dates, the authors conclude that the valley's first Neolithic millet farmers had settled there by c. 2000 BC, and initial copper mining and rudimentary smelting began in the late second millennium BC. This overlaps with the established dates for Southeast Asian metal-consumption sites, and provides an important new insight into the development of metallurgy in central Thailand and beyond.

The concentration of radiocarbon (14C) differs between ocean and atmosphere. Radiocarbon determinations from samples which obtained their 14C in the marine environment therefore need a marine-specific calibration curve and cannot be calibrated directly against the atmospheric-based IntCal20 curve. This paper presents Marine20, an update to the internationally agreed marine radiocarbon age calibration curve that provides a non-polar global-average marine record of radiocarbon from 0–55 cal kBP and serves as a baseline for regional oceanic variation. Marine20 is intended for calibration of marine radiocarbon samples from non-polar regions; it is not suitable for calibration in polar regions where variability in sea ice extent, ocean upwelling and air-sea gas exchange may have caused larger changes to concentrations of marine radiocarbon. The Marine20 curve is based upon 500 simulations with an ocean/atmosphere/biosphere box-model of the global carbon cycle that has been forced by posterior realizations of our Northern Hemispheric atmospheric IntCal20 14C curve and reconstructed changes in CO2 obtained from ice core data. These forcings enable us to incorporate carbon cycle dynamics and temporal changes in the atmospheric 14C level. The box-model simulations of the global-average marine radiocarbon reservoir age are similar to those of a more complex three-dimensional ocean general circulation model. However, simplicity and speed of the box model allow us to use a Monte Carlo approach to rigorously propagate the uncertainty in both the historic concentration of atmospheric 14C and other key parameters of the carbon cycle through to our final Marine20 calibration curve. This robust propagation of uncertainty is fundamental to providing reliable precision for the radiocarbon age calibration of marine based samples. We make a first step towards deconvolving the contributions of different processes to the total uncertainty; discuss the main differences of Marine20 from the previous age calibration curve Marine13; and identify the limitations of our approach together with key areas for further work. The updated values for ΔR, the regional marine radiocarbon reservoir age corrections required to calibrate against Marine20, can be found at the data base http://calib.org/marine/.

Radiocarbon (14C) ages cannot provide absolutely dated chronologies for archaeological or paleoenvironmental studies directly but must be converted to calendar age equivalents using a calibration curve compensating for fluctuations in atmospheric 14C concentration. Although calibration curves are constructed from independently dated archives, they invariably require revision as new data become available and our understanding of the Earth system improves. In this volume the international 14C calibration curves for both the Northern and Southern Hemispheres, as well as for the ocean surface layer, have been updated to include a wealth of new data and extended to 55,000 cal BP. Based on tree rings, IntCal20 now extends as a fully atmospheric record to ca. 13,900 cal BP. For the older part of the timescale, IntCal20 comprises statistically integrated evidence from floating tree-ring chronologies, lacustrine and marine sediments, speleothems, and corals. We utilized improved evaluation of the timescales and location variable 14C offsets from the atmosphere (reservoir age, dead carbon fraction) for each dataset. New statistical methods have refined the structure of the calibration curves while maintaining a robust treatment of uncertainties in the 14C ages, the calendar ages and other corrections. The inclusion of modeled marine reservoir ages derived from a three-dimensional ocean circulation model has allowed us to apply more appropriate reservoir corrections to the marine 14C data rather than the previous use of constant regional offsets from the atmosphere. Here we provide an overview of the new and revised datasets and the associated methods used for the construction of the IntCal20 curve and explore potential regional offsets for tree-ring data. We discuss the main differences with respect to the previous calibration curve, IntCal13, and some of the implications for archaeology and geosciences ranging from the recent past to the time of the extinction of the Neanderthals.

Early researchers of radiocarbon levels in Southern Hemisphere tree rings identified a variable North-South hemispheric offset, necessitating construction of a separate radiocarbon calibration curve for the South. We present here SHCal20, a revised calibration curve from 0–55,000 cal BP, based upon SHCal13 and fortified by the addition of 14 new tree-ring data sets in the 2140–0, 3520–3453, 3608–3590 and 13,140–11,375 cal BP time intervals. We detail the statistical approaches used for curve construction and present recommendations for the use of the Northern Hemisphere curve (IntCal20), the Southern Hemisphere curve (SHCal20) and suggest where application of an equal mixture of the curves might be more appropriate. Using our Bayesian spline with errors-in-variables methodology, and based upon a comparison of Southern Hemisphere tree-ring data compared with contemporaneous Northern Hemisphere data, we estimate the mean Southern Hemisphere offset to be 36 ± 27 14C yrs older.

Connecting calendar ages to radiocarbon (14C) ages, i.e. constructing a calibration curve, requires 14C samples that represent, or are closely connected to, atmospheric 14C values and that can also be independently dated. In addition to these data, there is information that can serve as independent tests of the calibration curve. For example, information from ice core radionuclide data cannot be directly incorporated into the calibration curve construction as it delivers less direct information on the 14C age–calendar age relationship but it can provide tests of the quality of the calibration curve. Furthermore, ice core ages on 14C-dated volcanic eruptions provide key information on the agreement of ice core and radiocarbon time scales. Due to their scarcity such data would have little impact if directly incorporated into the calibration curve. However, these serve as important “anchor points” in time for independently testing the calibration curve and/or ice-core time scales. Here we will show that such information largely supports the new IntCal20 calibration record. Furthermore, we discuss how floating tree-ring sequences on ice-core time scales agree with the new calibration curve. For the period around 40,000 years ago we discuss unresolved differences between ice core 10Be and 14C records that are possibly related to our limited understanding of carbon cycle influences on the atmospheric 14C concentration during the last glacial period. Finally, we review the results on the time scale comparison between the Greenland ice-core time scale (GICC05) and IntCal20 that effectively allow a direct comparison of 14C-dated records with the Greenland ice core data.

In much of Europe, the advent of low-input cereal farming regimes between c. ad 800 and 1200 enabled landowners—lords—to amass wealth by greatly expanding the amount of land under cultivation and exploiting the labour of others. Scientific analysis of plant remains and animal bones from archaeological contexts is generating the first direct evidence for the development of such low-input regimes. This article outlines the methods used by the FeedSax project to resolve key questions regarding the ‘cerealization’ of the medieval countryside and presents preliminary results using the town of Stafford as a worked example. These indicate an increase in the scale of cultivation in the Mid-Saxon period, while the Late Saxon period saw a shift to a low-input cultivation regime and probably an expansion onto heavier soils. Crop rotation appears to have been practised from at least the mid-tenth century.

Terrestrial plant macrofossils from the sedimentary record of Lake Suigetsu, Japan, provide the only quasi-continuous direct atmospheric record of radiocarbon (14C) covering the last 50 ka cal BP (Bronk Ramsey et al. 2012). Since then, new high precision data have become available on U-Th dated speleothems from Hulu Cave China, covering the same time range (Cheng et al. 2018). In addition, an updated varve-based chronology has also been published for the 2006 core from Lake Suigetsu (SG06) based on extended microscopic analysis of the sediments and improved algorithms for interpolation (Schlolaut et al. 2018). Here we reanalyze the radiocarbon dataset from Suigetsu based on the new varve counting information and the constraints imposed by the speleothem data. This enables the new information on the calendar age scale of the Suigetsu dataset to be used in the construction of the consensus IntCal calibration curve. Comparison of the speleothem and plant macrofossil records provides insight into the mechanisms underlying the incorporation of carbon into different types of record and the relative strengths of different types of archive for calibration purposes.

The Southern African Radiocarbon Database (SARD) is a new online, open-access database of published radiocarbon dates from southern African archaeological contexts. Compatible with the calibration, Bayesian modelling and mapping functionality of the OxCal software, the SARD will greatly assist in the documentation and analysis of chronological trends across the subcontinent. This article introduces the database and presents two case studies that demonstrate its utility and its integration with OxCal, comparing the temporal distribution of radiocarbon dates in two archaeologically well-investigated regions, and assessing the timing of Middle to Later Stone Age technological developments across the African subcontinent.