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.

The interaction of a solitary wave and a slowly varying mean background or flow for the Serre-Green-Naghdi (SGN) equations is studied using Whitham modulation theory. The exact form of the three SGN-Whitham modulation equations – two for the mean horizontal velocity and depth decoupled from one for the solitary wave amplitude field – is obtained in the solitary wave limit. Although the three equations are not diagonalizable, the restriction of the full system to simple waves for the mean equations is diagonalized in terms of Riemann invariants. The Riemann invariants are used to analytically describe the head-on and overtaking interactions of a solitary wave with a rarefaction wave and dispersive shock wave (DSW), leading to scenarios of solitary wave trapping or transmission by the mean flow. The analytical results for overtaking interactions prove that a simpler, approximate approach based on the DSW fitting method is accurate to the second order in solitary wave amplitude, beyond the first order accurate Korteweg-de Vries approximation. The analytical results also accurately predict the SGN DSW’s solitary wave edge amplitude and speed. The analytical results are favourably compared with corresponding numerical solutions of the full SGN equations. Because the SGN equations model the bi-directional propagation of strongly nonlinear, long gravity waves over a flat bottom, the analysis presented here describes large amplitudesolitary wave-mean flow interactions in shallow water waves.

The composition of phosgenite (ideal formula Pb2(CO3)Cl2, sp. gr. P4/mbm with a ≈ 8.15 and c ≈ 8.87 Å) from Monteponi Mine, Iglesias, Sardinia, Italy, its crystal structure and its high-T behaviour up to the onset of decomposition were investigated by a series of chemical analytical and diffraction techniques, including single-crystal X-ray (data collected at 293 K) and neutron diffraction (at 293 and 20 K), in situ high-T powder X-ray diffraction (XRD) and thermogravimetric analysis. Concentrations of >65 elements were measured. The empirical mineralogical formula of phosgenite, obtained by the multi-analytical approach used in this study, is almost identical to the ideal one, with only a few elements measured above the detection limit: Σ(Na2O+K2O+CaO+SiO2) = 0.11 wt.%. The concentration of other industrially relevant elements is insignificant. X-ray and neutron refinements, based on data collected at room T, confirm the previously reported general structural model of phosgenite, while providing a full description of the displacement parameters of all the atomic sites. The building unit of the crystal structure of phosgenite is represented by a Pb-polyhedron, in which Pb is coordinated by 5Cl + 4O (coordination number CN = 9), forming a monocapped square antiprism. The combination of face-sharing Pb-polyhedra generates dense layers parallel to (001), which are connected by (edge-sharing) CO3-groups to form the crystalline edifice. Low-T neutron diffraction data show evidence of a temperature-mediated phase transition towards a lower symmetry (space group P$\bar 4$), with a modest distortion of the building units of the structure. A tentative description of the low-T mechanisms, at the atomic scale, that can lead to the phase transition is provided.

The high-T behaviour of phosgenite proves this mineral is stable at least up to 523 K, at which the first evidence of transformation (with the coexistence of phosgenite + Pb2O2Cl, and probably an amorphous phase) takes place. The XRD pattern at 548 K unveils a more complex scenario, with coexisting: phosgenite (dominant) + Pb2O2Cl (minor) + mendipite [Pb3O2Cl2] (minor) + Pb5O2Cl6 (subordinate) (+ amorphous phase). This phase composition is preserved up to 648 K, after which phosgenite is no longer preserved, and the stable compounds are: mendipite [Pb3O2Cl2] (dominant), Pb2O2Cl (subordinate) + Pb5O2Cl6 (subordinate) + kutnohorite-type [Ca(Mn,Mg,Fe2+)(CO3)2] (likely, very minor) (+ amorphous phase). The same assemblage is observed up to 698 and back to 298 K after a decrease in T, showing an irreversible transformation of the pristine material. Therefore, the irreversible temperature-induced degradation of phosgenite is substantially governed by a decarbonation process.

The Kruskal–Friedman theorem asserts: in any infinite sequence of finite trees with ordinal labels, some tree can be embedded into a later one, by an embedding that respects a certain gap condition. This strengthening of the original Kruskal theorem has been proved by I. Kříž (Ann. Math. 1989), in confirmation of a conjecture due to H. Friedman, who had established the result for finitely many labels. It provides one of the strongest mathematical examples for the independence phenomenon from Gödel’s theorems. The gap condition is particularly relevant due to its connection with the graph minor theorem of N. Robertson and P. Seymour. In the present article, we consider a uniform version of the Kruskal–Friedman theorem, which extends the result from trees to general recursive data types. Our main theorem shows that this uniform version is equivalent both to $\Pi ^1_1$-transfinite recursion and to a minimal bad sequence principle of Kříž, over the base theory $\mathsf {RCA_0}$ from reverse mathematics. This sheds new light on the role of infinity in finite combinatorics.

We prove that the mapping class group is not an h-cobordism invariant of high-dimensional manifolds by exhibiting h-cobordant manifolds whose mapping class groups have different cardinalities. In order to do so, we introduce a moduli space of ‘h-block’ bundles and understand its difference with the moduli space of ordinary block bundles.