If A is in the p-Schatten class on ${\mathbb {R}}^n$, $1\leq p \leq {4n}/{(2n-1)}$, then the quantum translates of A are linearly independent. Moreover, there exists a nonzero operator in the p-Schatten class on ${\mathbb {R}}^n$, $p>{4n}/{(2n-1)}$, whose quantum translates are linearly dependent.

This article investigates the role of Catholic and non-Catholic local actors in shaping missionary activities in seventeenth-century Ottoman Europe. It examines jurisdictional conflicts and collaborations between Bosnian Franciscan friars, Ragusan merchants, Ottoman officials—particularly judges—and Serbian Orthodox clergy, whose interactions shaped the local landscape of Catholicism and defined the limits of Catholic engagement. Drawing primarily on Catholic missionary sources, the study argues that analysing missions through interconnected local, regional, and global lenses, while foregrounding the agency of local actors, provides a more nuanced understanding of early modern Catholicism. By expanding historiographical approaches that have primarily focused on Catholic missions outside Europe, the article advocates for the inclusion of Ottoman Europe as a significant yet understudied site of Catholic missionary activity. It further highlights the jurisdictional and institutional tensions within Catholic expansion and governance, revealing the complexities of missionary engagement in a politically fragmented and religiously plural environment.

Generative artificial intelligence (GenAI) shows promise for mental healthcare by increasing access to treatment. In this article, we analyse recent evidence on the use of GenAI chatbots as a treatment for common mental disorders. We examine key ethical and methodological considerations and discuss the specific risks for delusions. Adopting a precision psychiatry perspective, we propose that the therapeutic alliance can be improved by tailoring GenAI to mimic a user’s psychological traits, a version of socioaffective alignment.

Treatment-resistant schizophrenia (TRS) is a clinically challenging subtype of schizophrenia affecting up to 30% of patients, defined by persistent symptoms despite adequate trials of at least two antipsychotics. This review explores the complex neurobiology of TRS, highlighting the limitations of the dopamine hypothesis and emphasising the roles of glutamatergic, cholinergic and neurodevelopmental mechanisms. It outlines neuroimaging techniques (e.g. positron emission tomography, functional and structural magnetic resonance imaging, and proton magnetic resonance spectroscopy) used to explore neurotransmitter activity and structural brain changes in psychosis, and in TRS in particular, and gives an overview of their findings and utility. It also discusses frameworks like TRRIP and the INTEGRATE algorithm, which aim to facilitate earlier diagnosis and treatment. Integrating neuroimaging into practice may improve diagnosis and clinical outcomes and advance precision medicine approaches; emerging non-dopaminergic treatment options, such as xanomeline–trospium, may offer promising alternatives to standard clozapine treatment for TRS. Future research should prioritise biomarker discovery and the development of novel therapies beyond dopaminergic targets.

The impact of white-tailed deer browsing on crop yields, specifically soybean yield, has been a problem within agriculture for several decades. In an effort to reduce the losses incurred by deer browsing, several wildlife repellents have been commercialized and marketed for use on soybean. Despite their availability, limited research has been conducted on the ability of these repellents to deter feeding or the effects of these products on weed control when applied in combination with common herbicides. In 2023 and 2024, a field experiment was conducted in four soybean fields to evaluate five commercial deer repellent products (Bobbex, Hinder, Liquid Fence, Plantskydd+, and Penergetic bWV) for their ability to reduce deer browsing on soybean. Each product was applied either once, twice, or three times in conjunction with the preplant burndown, early postemergence, and late postemergence pesticide applications, respectively. Regular assessments of deer browsing were conducted at weekly intervals following applications. Across all locations in 2023 and 2024, all applications of repellent products, even three sequential applications of these products, failed to provide any consistent suppression in deer browsing throughout the growing season. An additional field experiment was conducted during both seasons to evaluate the potential impacts of combinations of common herbicides and deer repellents on weed control and soybean injury. Results from these trials indicate that very few differences in foxtail species, waterhemp, and common cocklebur control and crop injury were observed with any repellent and herbicide combination compared to treatments of post-emergent herbicides alone. Overall, the results from these experiments indicate that combinations of these deer repellent products with herbicides in tank mixtures do not increase or decrease weed control when compared to stand-alone herbicide treatments. There is also no evidence that these repellent products effectively deter deer browsing during the time frame when the soybean plant may be most vulnerable.

Solomon Islands’ plural legal system, in which customary law operates in parallel with common law, and its practice and effects on society have drawn scholarly attention in spaces of legal studies, policy, economics, and state governance. An area that remains understudied is the dynamic nature in which landowners use Indigenous cultural heritage such as ancestral sites or genealogies as kastom evidence in courts. We explore this intersection through a critical review of the literature, Solomon Islands court judgments, and the nation’s lacking cultural heritage legislation. Two major infrastructure development projects in Solomon Islands, the Tina Hydro Project located on Guadalcanal and the Bina-Talifu Project on Malaita, are also examined to explore the nuances of state-led compulsory versus negotiated land acquisition. Fueling the perception that the customary land system is more of a hinderence than a strength to its peoples, these case studies demonstrate the fluid and unpredictable nature with which kastom evidence has been implemented in legal forums to substantiate or dispute claims. Ultimately, we argue that this largely reflects an incongruence between the British legal framework and traditional land tenure systems. Furthermore, we highlight how greater integration of archaeological expertise into legal processes of land surveying in Solomon Islands has the potential to mitigate some of these challenges.

Syncope in children is commonly benign, yet rare cardiovascular anomalies may be causative. We present a child with recurrent syncope, ultimately diagnosed with an aorto-right atrial connection. Transcatheter closure was successfully performed with an Amplatzer Duct Occluder II. This case emphasizes considering aorto-atrial connections in pediatric syncope with continuous murmurs and highlights the efficacy of percutaneous closure.

This paper outlines a structured bibliometric methodology for analyzing rural history as a scholarly field from 1989 to 2025. Drawing from Scopus, a filtered dataset of 436 research articles was compiled through a multi-phase selection process focused on thematic and disciplinary relevance. Using tools such as CiteSpace, VOSviewer, and bibliometrix (R), the study explores patterns in authorship, citations, and keyword usage, offering insights into the field’s development. The findings demonstrate a clear shift from traditional European agrarian narratives toward more diverse, global, and interdisciplinary approaches, integrating themes from cultural history, political ecology, and spatial analysis. Clustering and trend analyses reveal how rural history has evolved methodologically and conceptually, moving beyond its empirical foundations toward more critical and multi-scalar perspectives. This framework offers a replicable model for future historiographical assessments and contributes to understanding the role of rural history within broader academic discourse.

To better understand the dependence of the magnetic field structure in the plasma edge on the plasma boundary shape, in the context of X-point and island divertor designs, we define and develop a class of stellarators called umbilic stellarators. These equilibria are characterised by a single continuous high-curvature edge on the plasma boundary that goes around multiple times toroidally before meeting itself. We develop a technique that allows us to simultaneously optimise the plasma boundary along with a curve lying on the boundary on which we impose a high curvature while imposing omnigenity – a property of the magnetic field that ensures trapped particle confinement throughout the plasma volume. We find that umbilic stellarators naturally tend to favour piecewise omnigenity instead of omnigenity with a specific helicity. After generating omnigenous umbilic stellarators, we design coil sets for some of them and explore the fieldline structure in the edge and its sensitivity to small fluctuations in the plasma. Finally, using single-stage optimisation, we simultaneously modify the plasma and coil shape and propose an experiment to modify an existing tokamak to a finite-$\beta$ stellarator using this technique and explore a potentially simpler way to convert a limited tokamak into a diverted stellarator.

In psychometric sciences, such as social or behavioral sciences, and, similarly, in medical sciences, it is increasingly common to deal with longitudinal data organized as high-dimensional multidimensional arrays, also known as tensors. Within this framework, the time-continuous property of longitudinal data often implies a smooth functional structure on one of the tensor modes. To help researchers investigate such data, we introduce a new tensor decomposition approach based on the PARAFAC decomposition. Our approach allows researchers to represent a high-dimensional functional tensor as a low-dimensional set of functions and feature matrices. Furthermore, to capture the underlying randomness of the statistical setting more efficiently, we introduce a probabilistic latent model in the decomposition. A covariance-based block-relaxation algorithm is derived to obtain estimates of model parameters. Thanks to the covariance formulation of the solving procedure and thanks to the probabilistic modeling, the method can be used in sparse and irregular sampling schemes, making it applicable in numerous settings. Our approach is applied in the psychometric setting to help characterize multiple neurocognitive scores observed over time in the Alzheimer’s Disease Neuroimaging Initiative study. Finally, intensive simulations show a notable advantage of our method in reconstructing tensors.

This article offers an eyewitness, Venezuelan account of the United States’ January 3 military intervention to extract Nicolás Maduro, situating the operation within a longer history of U.S. hemispheric dominance. It asks how this unprecedented drone- and airpower-based assault reshapes Venezuelan politics, regional dynamics, and the emerging global order. Combining narrative testimony from Caracas with historical context, the piece argues that the intervention revives a Roosevelt Corollary-style logic of policing Latin America while simultaneously legitimizing a more anarchic, sphere-of-influence world. The article concludes that only a transition that empowers Venezuela’s democratic actors can render the intervention legitimate in terms of sovereignty, human rights, and freedom.

This study examines the utterance-initial prosodic marking of sarcasm in English and its perception in listeners who did and listeners who did not self-identify as being on the autism spectrum. We ask (i) whether speakers use prosody to mark sarcasm in the early, ‘pre-target’ portion of an utterance (that is, in the portion before a ‘target’ word most closely associated with the sarcastic intent occurs), (ii) whether individuals vary in how they mark sarcasm, (iii) whether listeners reliably recognize sarcasm from pre-target prosody alone, and (iv) whether recognition accuracy varies by speaker or self-identified autistic traits. Eight American English speakers were recorded producing utterances presented in contexts conducive to either sarcasm or sincerity. Pre-target parts were presented in a two-alternative forced-choice experiment to individuals who either did (n=51) or did not (n=44) self-identify as being on the autism spectrum, and were examined for syllable duration and f0-related properties (maximum, minimum, range, and wiggliness). Results show that speakers distinguish sarcasm and sincerity in the pre-target region with duration being the most salient marker. Most listeners recognize sarcasm from pre-target fragments, but there is variation in how well each speaker is perceived. Whether the listener self-identified as being on the autism spectrum or not does not predict sarcasm and sincerity recognition accuracy. The results provide evidence that utterance-initial prosody contributes to sarcasm recognition, with the proviso that speaker and listener variation be taken into account.