We consider the hypergraph Turán problem of determining $ex(n, S^d)$, the maximum number of facets in a $d$-dimensional simplicial complex on $n$ vertices that does not contain a simplicial $d$-sphere (a homeomorph of $S^d$) as a subcomplex. We show that if there is an affirmative answer to a question of Gromov about sphere enumeration in high dimensions, then $ex(n, S^d) \geq \Omega (n^{d + 1 - (d + 1)/(2^{d + 1} - 2)})$. Furthermore, this lower bound holds unconditionally for 2-LC (locally constructible) spheres, which includes all shellable spheres and therefore all polytopes. We also prove an upper bound on $ex(n, S^d)$ of $O(n^{d + 1 - 1/2^{d - 1}})$ using a simple induction argument. We conjecture that the upper bound can be improved to match the conditional lower bound.

We investigated the interactive effects of bilingualism and sleep on executive functioning at the behavioral level. We conducted two experiments using two independent samples of bilingual young adults, the Flanker task to assess executive performance, the Pittsburg Sleep Quality Index to measure retrospective sleep quality over a one-month period and the Insomnia Severity Index to assess insomnia-related symptoms. In Experiment 1, we registered bilingualism effects on executive performance in poor, but not in good sleepers. In Experiment 2, the magnitude of bilingual effects increased with increasing severity of insomnia symptoms. We conclude that when poor sleep quality and insomnia negatively affect cognitive resources, bilingualism-related cognitive effects emerge more prominently. This suggests higher degrees of bilingualism may compensate detrimental effects of poor sleep quality and insomnia on executive functioning. We suggest that cognitive research in bilingualism and sleep could benefit from controlling for interindividual variability in sleep quality and vice versa.

In 2025, the United States raised tariffs to rates not seen for more than a century. These tariffs were not part of a carefully designed industrial strategy. Instead, the second Trump administration distanced itself from existing industrial policy initiatives and indicated a desire to roll back government-funded subsidies for businesses. This article examines the rationale behind the United States’ pivot from subsidies to tariffs and explores implications for trade partners and multilateral institutions.

Digital eXtended Reality technologies enable users to view and interact with spaces and objects in three dimensions (3D), thus supporting a variety of potential innovative embodied applications in archaeology. Here, we review the Apple Vision Pro as a Mixed/Augmented Reality (MR/AR) headset to determine where it might fit within current archaeological practice. Our interest in this device spans primary field data collection, in situ visual–spatial interpretation, and public education and tourism. Overall, we find that although it makes certain advances on prior eXtended Reality hardware, it does not yet represent a significant enough shift forward to have a major impact on archaeology. However, we do plan to continue our field experiments with this technology to push its limits and to prepare for future improvements to this product and its competitors.

Emerging infectious diseases pose threats to wildlife, particularly in geographically isolated populations where hosts may lack prior exposure and immunity. Seabirds inhabiting remote islands in the southwest Atlantic and Southern Ocean, including threatened albatrosses and petrels, are increasingly affected by infectious pathogens. However, baseline data on vector-borne infections in these species remain scarce. This study assessed the presence of vector-borne haemosporidian parasites (Plasmodium, Haemoproteus and Leucocytozoon) and bacterial pathogens (Borrelia burgdorferi sensu lato, Anaplasma and Ehrlichia) in albatrosses and petrels, providing insights into disease prevalence and potential threats to these populations. We analysed blood and tissue samples from 269 individuals of 5 albatross and 12 petrel species, collected over an 11-year period (2013–2023) from South Georgia and multiple sites along the Brazilian coastline. Molecular assays, including nested Polymerase Chain Reaction (PCR), were used for pathogen screening. Blood smears from birds sampled in South Georgia were also examined for haemoparasites via light microscopy. We found no molecular or microscopy evidence of infection with haemosporidian parasites, Borrelia, Anaplasma or Ehrlichia in any of the samples. These findings suggest that vector-borne pathogens are either absent or at low prevalence, possibly because of limited vector presence, natural resistance or historical isolation from infection. Continuous monitoring is critical given current environmental changes and risks of pathogen introduction via climate-driven shifts in vector distribution. Our study establishes an essential baseline for future disease surveillance, prevention and mitigation in albatrosses and petrels, underscoring the importance of long-term monitoring to detect emerging pathogens in vulnerable seabird populations.

A simple view about “now” is that it picks out the time of the speech act in which it is used. A major advantage of this view is that it incorporates a semantical claim about reference in the larger framework of speech acts. However, the view cannot account for uses of “now” in so-called “answering machine” cases of speech acts, where we lack both clear intuitions and a widely accepted metaphysical view about their temporal locations. I first show that this problem is not limited to indexicals and answering machines. I then propose a different token-reflexive, speech act-friendly view: that speakers set detonation conditions for tokens of “now”, which, when the conditions are met, pick out the time of their detonation.

Many scholars now contend that the wall separating church and state has been effectively dismantled. One of the strongest pieces of evidence used to make this argument is the transfer of over five million taxpayer dollars to churches during Covid-19. But who exactly received this money? When the wall separating church and state came crashing down, as some assert, was there an ambush of religious actors seeking to collect federal funds? Or did we see many religious actors maintain their distance? What distinguishes one group from the other? This research note examines the behavior of religious congregations during Covid-19 with regard to the Paycheck Protection Program (PPP). We compare a sample of 2020 and 2021 PPP congregation recipients with the 2020 US Religious Census to note which denominations are over- and under-represented and then test the hypotheses suggested by the existing literature on faith-based organizations and government funding.

We establish a one-to-one correspondence between Kähler metrics in a given conformal class and parallel sections of a certain vector bundle with conformally invariant connection, where the parallel sections satisfy a set of non-linear algebraic constraints that we describe. The vector bundle captures 2-form prolongations and is isomorphic to $\Lambda^3(\mathcal{T})$, where ${\mathcal{T}}$ is the tractor bundle of conformal geometry, but the resulting connection differs from the normal tractor connection by curvature terms.

Our analysis leads to a set of obstructions for a Riemannian metric to be conformal to a Kähler metric. In particular, we find an explicit algebraic condition for a Weyl tensor which must hold if there exists a conformal Killing–Yano tensor, which is a necessary condition for a metric to be conformal to Kähler. This gives an invariant characterization of algebraically special Riemannian metrics of type D in dimensions higher than four.

QuickSelect (also known as Find), introduced by Hoare ((1961) Commun. ACM 4 321–322.), is a randomized algorithm for selecting a specified order statistic from an input sequence of $n$ objects, or rather their identifying labels usually known as keys. The keys can be numeric or symbol strings, or indeed any labels drawn from a given linearly ordered set. We discuss various ways in which the cost of comparing two keys can be measured, and we can measure the efficiency of the algorithm by the total cost of such comparisons.

We define and discuss a closely related algorithm known as QuickVal and a natural probabilistic model for the input to this algorithm; QuickVal searches (almost surely unsuccessfully) for a specified population quantile $\alpha \in [0, 1]$ in an input sample of size $n$. Call the total cost of comparisons for this algorithm $S_n$. We discuss a natural way to define the random variables $S_1, S_2, \ldots$ on a common probability space. For a general class of cost functions, Fill and Nakama ((2013) Adv. Appl. Probab. 45 425–450.) proved under mild assumptions that the scaled cost $S_n / n$ of QuickVal converges in $L^p$ and almost surely to a limit random variable $S$. For a general cost function, we consider what we term the QuickVal residual:

\begin{equation*} \rho _n \,{:\!=}\, \frac {S_n}n - S. \end{equation*}

The residual is of natural interest, especially in light of the previous analogous work on the sorting algorithm QuickSort (Bindjeme and Fill (2012) 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), Discrete Mathematics, and Theoretical Computer Science Proceedings, AQ, Association: Discrete Mathematics and Theoretical Computer Science, Nancy, pp. 339–348; Neininger (2015) Random Struct. Algorithms 46 346–361; Fuchs (2015) Random Struct. Algorithms 46 677–687; Grübel and Kabluchko (2016) Ann. Appl. Probab. 26 3659–3698; Sulzbach (2017) Random Struct. Algorithms 50 493–508). In the case $\alpha = 0$ of QuickMin with unit cost per key-comparison, we are able to calculate–àla Bindjeme and Fill for QuickSort (Bindjeme and Fill (2012) 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), Discrete Mathematics and Theoretical Computer Science Proceedings, AQ, Association: Discrete Mathematics and Theoretical Computer Science, Nancy, pp. 339–348.)–the exact (and asymptotic) $L^2$-norm of the residual. We take the result as motivation for the scaling factor $\sqrt {n}$ for the QuickVal residual for general population quantiles and for general cost. We then prove in general (under mild conditions on the cost function) that $\sqrt {n}\,\rho _n$ converges in law to a scale mixture of centered Gaussians, and we also prove convergence of moments.