Numerous applications in psychological research require that a data set is partitioned via the inverse of a clustering criterion. This anticlustering seeks for high similarity between groups (maximum diversity) or high pairwise dissimilarity within groups (maximum dispersion). Brusco et al. (2020) proposed a bicriterion heuristic (BILS) that simultaneously seeks for maximum diversity and dispersion, introducing the bicriterion approach for anticlustering. We investigate if the bicriterion approach can be improved using exact algorithms that guarantee globally optimal criterion values. Despite the theoretical computational intractability of anticlustering, we present a new exact algorithm for maximum dispersion that scales to quite large data sets ($N = 1,000$). However, a fully exact bicriterion approach was only feasible for small data sets (about $N = 30$). We therefore developed hybrid approaches that maintain optimal dispersion but use heuristics to maximize diversity on top of it. In a simulation study and an example application, we compared several hybrid approaches. An adaptation of BILS that initiates each iteration with a partition having optimal dispersion (BILS-Hybrid-All) performed best across a variety of data inputs. All of the methods developed here as well as the original BILS algorithm are available via the free and open-source R package anticlust.

Paleontology provides insights into the history of the planet, from the origins of life billions of years ago to the biotic changes of the Recent. The scope of paleontological research is as vast as it is varied, and the field is constantly evolving. In an effort to identify “Big Questions” in paleontology, experts from around the world came together to build a list of priority questions the field can address in the years ahead. The 89 questions presented herein (grouped within 11 themes) represent contributions from nearly 200 international scientists. These questions touch on common themes including biodiversity drivers and patterns, integrating data types across spatiotemporal scales, applying paleontological data to contemporary biodiversity and climate issues, and effectively utilizing innovative methods and technology for new paleontological insights. In addition to these theoretical questions, discussions touch upon structural concerns within the field, advocating for an increased valuation of specimen-based research, protection of natural heritage sites, and the importance of collections infrastructure, along with a stronger emphasis on human diversity, equity, and inclusion. These questions offer a starting point—an initial nucleus of consensus that paleontologists can expand on—for engaging in discussions, securing funding, advocating for museums, and fostering continued growth in shared research directions.

Given positive Radon measures, $\mu $ and $\lambda $, on the complex unit circle, we show that absolute continuity of $\mu $ with respect to $\lambda $ is equivalent to their reproducing kernel Hilbert spaces of “analytic Cauchy transforms” in the complex unit disk having dense intersection in the space of $\mu $-Cauchy transforms.

A realization is a triple, $(A,b,c)$, consisting of a $d-$tuple, $A= (A_1, \cdots , A_d )$, $d\in \mathbb {N}$, of bounded linear operators on a separable, complex Hilbert space, $\mathcal {H}$, and vectors $b,c \in \mathcal {H}$. Any such realization defines an analytic non-commutative (NC) function in an open neighbourhood of the origin, $0:= (0, \cdots , 0)$, of the NC universe of $d-$tuples of square matrices of any fixed size. For example, a univariate realization, i.e., where A is a single bounded linear operator, defines a holomorphic function of a single complex variable, z, in an open neighbourhood of the origin via the realization formula $b^{*} (I-zA)^{-1} c$.

It is well known that an NC function has a finite-dimensional realization if and only if it is a non-commutative rational function that is defined at $0$. Such finite realizations contain valuable information about the NC rational functions they generate. By extending to infinite-dimensional realizations, we construct, study and characterize more general classes of analytic NC functions. In particular, we show that an NC function is (uniformly) entire if and only if it has a jointly compact and quasinilpotent realization. Restricting our results to one variable shows that a formal Taylor series extends globally to an entire or meromorphic function in the complex plane, $\mathbb {C}$, if and only if it has a realization whose component operator is compact and quasinilpotent, or compact, respectively. This motivates our definition of the field of global (uniformly) meromorphic NC functions as the field of fractions generated by NC rational expressions in the ring of NC functions with jointly compact realizations. This definition recovers the field of meromorphic functions in $\mathbb {C}$ when restricted to one variable.

Kinship can be difficult to discern in the archaeological record, but the study of ancient DNA offers a useful window into one form of kinship: biological relatedness. Here, the authors explore possible kin connections at the post-Roman site of Worth Matravers in south-west England. They find that, while clusters of genetically related individuals are apparent, the inclusion of unrelated individuals in double or triple burials demonstrates an element of social kinship in burial location. Some individuals also carried genetic signatures of continental ancestry, with one young male revealing recent West African ancestry, highlighting the diverse heritage of early medieval Britain.

Sít’ Tlein (Malaspina Glacier), located in Southeast Alaska, has a complex flow history. This piedmont glacier, the largest in the world, is fed by three main tributaries that all exhibit similar flow patterns, yet with varying surge cycles. The piedmont lobe is dramatically reshaped by surges that occur at approximately decadal timescales. By combining historical accounts with modern remote sensing data, we derive a surge history over the past century. We leverage the Stochastic Matrix Factorization, a novel data analysis and interpolation technique, to process and interpret large datasets of glacier surface velocities. A variant of the Principal Component Analysis allows us to uncover spatial and temporal patterns in ice dynamics. We show that Sít’ Tlein displays a wide range of behaviors, spanning quiescence to surge with seasonal to decadal variations of ice flow direction and magnitude. We find that in the lobe, surges dominate the velocity dataset’s variance (spanning 1984–2021), while seasonal variations represent a much smaller part of the variance. However, despite the regular surge pulses, the glacier lobe is far from equilibrium, and widespread retreat of the glacier is inevitable, even without further climate warming.

High-power fiber lasers generate local heat load extremes during their operation, which increase the fiber temperature and lead to adverse thermal effects, such as transverse mode instability or cladding/coating thermal damage. The local temperature extremes are usually located near the end of a fiber where the pump power is delivered. In this paper, longitudinally inhomogeneous doping concentration profiles are applied to reduce the heat load extremes. Utilizing a new degree of freedom, it is shown by both simulations and measurements that the maximal temperature along the fiber can be effectively decreased by using active fibers with an increasing concentration profile in the direction of the pumping power. The concept is studied by a comprehensive numerical model that considers temperature-dependent parameters and is also demonstrated by measurement on an in-house built thulium-doped fiber laser formed by spliced sections with different concentrations. The output power of 54 W with the slope efficiency exceeding 62% was reached.

The First Large Absorption Survey in H i (FLASH) is a large-area radio survey for neutral hydrogen in and around galaxies in the intermediate redshift range $0.4\lt z\lt1.0$, using the 21-cm H i absorption line as a probe of cold neutral gas. The survey uses the ASKAP radio telescope and will cover 24,000 deg$^2$ of sky over the next five years. FLASH breaks new ground in two ways – it is the first large H i absorption survey to be carried out without any optical preselection of targets, and we use an automated Bayesian line-finding tool to search through large datasets and assign a statistical significance to potential line detections. Two Pilot Surveys, covering around 3000 deg$^2$ of sky, were carried out in 2019-22 to test and verify the strategy for the full FLASH survey. The processed data products from these Pilot Surveys (spectral-line cubes, continuum images, and catalogues) are public and available online. In this paper, we describe the FLASH spectral-line and continuum data products and discuss the quality of the H i spectra and the completeness of our automated line search. Finally, we present a set of 30 new H i absorption lines that were robustly detected in the Pilot Surveys, almost doubling the number of known H i absorption systems at $0.4\lt z\lt1$. The detected lines span a wide range in H i optical depth, including three lines with a peak optical depth $\tau\gt1$, and appear to be a mixture of intervening and associated systems. Interestingly, around two-thirds of the lines found in this untargeted sample are detected against sources with a peaked-spectrum radio continuum, which are only a minor (5–20%) fraction of the overall radio-source population. The detection rate for H i absorption lines in the Pilot Surveys (0.3 to 0.5 lines per 40 deg$^2$ ASKAP field) is a factor of two below the expected value. One possible reason for this is the presence of a range of spectral-line artefacts in the Pilot Survey data that have now been mitigated and are not expected to recur in the full FLASH survey. A future paper in this series will discuss the host galaxies of the H i absorption systems identified here.