This paper investigates sharp stability estimates for the fractional Hardy–Sobolev inequality:

\begin{align*}\ \ \ \ \ \ \ \ \ \mu_{s,t}\left(\mathbb{R}^N\right) \left(\int_{\mathbb{R}^N} \frac{|u|^{2^*_s(t)}}{|x|^t} \,\mathrm{d}x \right)^{\frac{2}{2^*_s(t)}} \leq \int_{\mathbb{R}^N} \left|(-\Delta)^{\frac{s}{2}} u \right|^2 \,\mathrm{d}x, \quad \text{for all } u \in \dot{H}^s\left(\mathbb{R}^N\right)\end{align*}

where $s \in (0,1)$, $0 \lt t \lt 2s$, $N \gt 2s$ is an integer, and $2^*_s(t) = \frac{2(N-t)}{N-2s}$. Here, $\mu_{s,t}\left(\mathbb{R}^N\right)$ represents the best constant in the inequality. The primary focus is on the quantitative stability results of the above inequality and the corresponding Euler–Lagrange equation near a positive ground-state solution. Additionally, a qualitative stability result is established for the Euler–Lagrange equation, offering a thorough characterization of the Palais–Smale sequences for the associated energy functional. These results generalize the sharp quantitative stability results for the classical Sobolev inequality in $\mathbb{R}^N$, originally obtained by Bianchi and Egnell [J. Funct. Anal. 1991] as well as the corresponding critical exponent problem in $\mathbb{R}^N$, explored by Ciraolo, Figalli, and Maggi [Int. Math. Res. Not. 2017] in the framework of fractional calculus.

Maternal consumption of a high-fat diet (mHFD) during perinatal life influences hypothalamic-pituitary-adrenal (HPA) axis activation and impacts the long-term physiological and metabolic health of offspring. Milk-derived extracellular vesicles (MEVs) are lipid-coated nanovesicles that transfer biological materials from mother to infant and can survive intestinal degradation and cross the blood-brain barrier. MEVs provide cytoprotection in peripheral organs; however, their pro-survival functions remain unknown in the neonatal brain. Further, sex differences resulting from MEV treatment require investigation, as male and female neonates display variable responses to early life nutrient stress. We investigated the interaction between MEVs and the heat shock protein response in the liver, hypothalamus, and prefrontal cortex in male and female neonatal rats exposed to perinatal mHFD at postnatal day 11. MEV treatment robustly modulated the HSR in female neonates with the largest response recorded in the prefrontal cortex. These results suggest that MEVs may influence pro-survival outcomes in the prefrontal cortex by activating HSF1-mediated pro-survival in a sex-specific manner.

User engagement remains a challenge in digital mental health. This editorial reconsiders engagement as a process rather than an outcome, introducing a four-step model to define, measure and link engagement to outcomes. The approach promotes standardisation, interpretability and scalability, advancing the science and implementation of digital health interventions.

We study conformal product structures on compact reducible Riemannian manifolds, and show that under a suitable technical assumption, the underlying Riemannian manifolds are either conformally flat or local triple products, i.e., locally isometric to Riemannian manifolds of the form $(M,g)$ with $M=M_1\times M_2\times M_3$ and $g=e^{2f}g_1+g_2+g_3$, where $g_i$ is a Riemannian metric on $M_i$, for $i\in \{1,2,3\}$, and $f\in C^\infty (M_1\times M_2)$.

The Paleolithic period encompasses the oldest material in the archaeological record and spans some three million years. Because of its antiquity, competition for the earliest evidence of behaviors or phenomena can be intense. Paleolithic archaeology has therefore been seen as having a competitive atmosphere that was often hostile to female practitioners. In addition, female archaeologists who choose to undertake the role of field director—one of the most visible and influential roles in Paleolithic archaeology—face significant hurdles such as sexism and impediments related to motherhood. In this article, we investigate whether the perception of male bias in Paleolithic archaeology is valid. To do this, we assessed the gender demographics of Paleolithic archaeologists in tenure-track positions in North American institutions, publication rates by gender for articles on the Paleolithic, and the gender of archaeologists identified as “experts” in human evolution documentaries aired on PBS from 1994 to 2023. We found that gender demographics in Paleolithic archaeology follow that of the larger field of archaeology, with a stark imbalance at the rank of full professor but increasing gender parity at the lower ranks. Men outpublish women in all five journals we studied, but there is a positive trend over time. In contrast, the percentage of women “experts” featured in documentaries on human evolution never rose above 23%, with very little change over time.

Notocotylidae is a family of digeneans with some aberrant morphological features (absence of ventral sucker), which as sexual adults parasitise herbivorous and molluscivorous birds and mammals. The phylogenetics and taxonomy of this family have many unresolved problems concerning the relatedness of genera and species and the reliability of identification of specimens for which molecular data are available. The aim of this study is morphological and molecular characterisation of the type species of Notocotylus Diesing, 1839 (Notocotylus triserialis Diesing, 1839) and its two congeners, Notocotylus pacifera (Noble, 1933) and Notocotylus sp., and verification of the monophyly of the genus Notocotylus within the taxonomic boundaries established in the recent revision. Notocotylus triserialis was collected from a Greater White-fronted Goose Anser albifrons (Scopoli, 1769) taken down in the Russian Karelia, and the other two digenean species were derived from European Coots Fulica atra Linnaeus, 1758, from different locations in Eurasia (Eastern Europe and the Far East). We provide detailed morphological descriptions of the examined digeneans, supplemented with original line drawings. Notocotylus sp. is morphologically similar to N. pacifera but differs in cirrus sac length. Phylogenetic inference based on the 28S rRNA gene dataset places N. triserialis within a well-supported clade comprising several congeners, whereas N. pacifera is recovered outside this assemblage, forming a closer phylogenetic association with Pseudocatatropis dvoryadkini Izrailskaia, Besprozvannykh, Tatonova, Nguyen and Ngo, 2019. Thus, our data do not support the monophyly of the genus Notocotylus.

In the early nineteenth century, foreign explorers traveling throughout Mexico and Central America began documenting sites, structures, and monuments then unknown in the United States and Europe. These explorers depicted the ruins they encountered as deserted and lifeless and suggested that the passage of time had rendered them ineffective. This article challenges such a Western, Romantic understanding of Maya ruins. Drawing on ruination studies and the material turn, it argues instead that Maya ruins are affective, consequential, and shape human actions. To do so, the article briefly considers the utility of assemblage theory and Indigenous ontologies to archaeological interpretations of ruins. It then takes as a case study an intrasite sak-be at Punta Laguna, Yucatán, México, and interprets it as a kuxansum—an Indigenous Maya concept of a living rope of blood that, even when seemingly severed, continues to connect spaces, human and other-than-human entities, and various temporalities. This interpretation encourages scholars to question whether broken or seemingly abandoned ruins such as roads must always be interpreted as functionally obsolete or whether new meanings are often made from the old.

Although insect pollination has been shown to enhance yields of soybean, Glycine max (Linnaeus) Merrill (Fabaceae), the lingering misconception among growers that soybean does not benefit from insect pollination hinders the adoption of pollinator-friendly practices. As such, identifying the wild pollinators visiting soybean flowers can help raise awareness of their importance in soybean production. We surveyed wild bees and wasps visiting soybean flowers and carrying soybean pollen in an extensive field crop region of southeastern Canada (Ontario and Quebec). Insects were hand-netted from 19 soybean fields while they actively foraged on soybean flowers, and their corbicular or scopal loads and body surfaces were screened for soybean pollen. A total of 81 insects (77 wild bees and four wasps), representing 18 bee and four wasp species, were collected. The majority (91.4%) carried soybean pollen, indicating a potential role in soybean pollination. Generalist bumble bees and ground-nesting bees were the most common, suggesting that management practices that support these two groups are likely to be particularly relevant for growers in Canada.

Trichinella spiralis (T. spiralis) is a zoonotic parasitic worm that has a significant impact on both public health and the livestock industry. It is widely used in experimental studies because of several unique features of its life cycle that can be completed in a single host, including distinct intestinal and muscular phases of infection, and it can be easily maintained in laboratory animals. These characteristics make T. spiralis a valuable model for evaluating the efficacy of new drugs and vaccines against parasitic infections. The current work aims to evaluate the procedures used for Trichinella larval counting in experimental studies by comparing the magnetic stirring digestion method (MSDM) with individual muscle digestion and compression techniques under standardised, controlled conditions to assess their effectiveness and applicability. Fifteen male Swiss albino mice were orally infected with T. spiralis and sacrificed on day 35 post-infection. They were divided into three groups: group 1—MSDM for total larval count; group 2—individual digestion of masseter, diaphragm, gastrocnemius, and tongue muscles; and group 3—slide compression method of the same muscles. MSDM yielded the highest larval counts, with individual muscle digestion and compression methods generally producing significantly lower results, except tongue digestion, while correlation and concordance analyses identified gastrocnemius compression as an alternative despite overall poor agreement with the reference method. Therefore, MSDM is the most accurate method for larval counting in experimental studies, compared to individual muscle digestion or compression methods.

This paper proposes constructing a new series of Brazilian sugar imports to Portugal between 1761 and 1807. The new customs data collected provides quantities, Brazilian origin, quality and taxes of the sugar. Based on the results of the empirical research, we demonstrate and corroborate the Brazilian sugar renaissance in the second half of the eighteenth century, a period of crisis in the colony’s mining industry and in the Portuguese trade balance. The growth of the sugar economy in the colony contributed to the adjustment of Portugal’s external accounts. The new information has allowed us to verify the increase in Brazilian sugar exports, especially after the early 1770s, despite the stagnation of the Portuguese economy.

We consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown parameters of interest by proving a law of large numbers for associated variation functionals. In contrast to the semimartingale setting, the optimal window size for pre-averaging depends on the unknown roughness parameter of the underlying process. We evaluate the performance of our estimators in a simulation study and use them to empirically verify Kolmogorov’s $2/3$-law in turbulence data contaminated by instrument noise.

Let $\{X_{i}\}_{i\geq1}$ be a sequence of independent and identically distributed random variables and $T\in\{1,2,\ldots\}$ a stopping time associated with this sequence. In this paper, the distribution of the minimum observation, $\min\{X_{1},X_{2},\ldots,X_{T}\}$, until the stopping time T is provided by proposing a methodology based on an appropriate change of the initial probability measure of the probability space to a truncated (shifted) one on the $X_{i}$. As an application of the aforementioned general result, the random variables $X_{1},X_{2},\ldots$ are considered to be the interarrival times (spacings) between successive appearances of events in a renewal counting process $\{Y_{t},t\geq0\}$, while the stopping time T is set to be the number of summands until the sum of the $X_{i}$ exceeds t for the first time, i.e. $T=Y_{t}+1$. Under this setup, the distribution of the minimal spacing, $D_{t}=\min\{X_{1},X_{2},\ldots,X_{Y_{t}+1}\}$, that starts in the interval [0, t] is investigated and a stochastic ordering relation for $D_{t}$ is obtained. In addition, bounds for the tail probability of $D_{t}$ are provided when the interarrival times have the increasing failure rate / decreasing failure rate property. In the special case of a Poisson process, an exact formula, as well as closed-form bounds and an asymptotic result, are derived for the tail probability of $D_{t}$. Furthermore, for renewal processes with Erlang and uniformly distributed interarrival times, exact and approximation formulae for the tail probability of $D_{t}$ are also proposed. Finally, numerical examples are presented to illustrate the aforementioned exact and asymptotic results, and practical applications are briefly discussed.

After reviewing several stances in modern theology on the historicity of the resurrection of Jesus, this article argues that a common feature of the worldviews of Baroque Catholicism, classical Reformation theology, and the Enlightenment, namely, their separation of the supernatural and natural realms into ‘two orders’, explains the attractiveness of the apologetical strategy of affirming the reality of the resurrection as a non-historical, supernatural event. Drawing on the temporal and spatial imaginary of Henri de Lubac’s theology of grace, it concludes by pressing the case for a theological understanding of the resurrection of Jesus as a historical event that valorises the eschatological resonance of time.