Confinement quality in fusion plasma is influenced significantly by the presence of heavy impurities, which can lead to radiative heat loss and reduced confinement. This study explores the clustering of heavy impurity, i.e. tungsten in edge plasma, using high-resolution direct numerical simulations of the Hasegawa–Wakatani equations. We use the Stokes number to quantify the inertia of impurity particles. It is found that particle inertia will cause spatial intermittency in particle distribution and the formation of large-scale structures, i.e. the clustering of particles. The degrees of clustering are influenced by the Stokes number. To quantify these observations, we apply a modified Voronoi tessellation, which assigns specific volumes to impurity particles. By determining time changes of these volumes, we can calculate the impurity velocity divergence, which allows the clustering dynamics to be assessed. To quantify the clustering statistically, several approaches are applied, such as probability density function (PDF) of impurity velocity divergence and joint PDF of volume and divergence.

Lewy body dementias (LBD) are the second most common dementia. Several genes have been associated with LBD, but little is known about their contributions to LBD pathophysiology. Each gene may transcribe multiple RNA, and LBD brains have extensive RNA splicing dysregulation. Hence, we completed the first transcriptome-wide transcript-level differential expression analysis of post-mortem LBD brains for gaining more insights into LBD molecular pathology that are essential for facilitating discovery of novel therapeutic targets and biomarkers for LBD. We completed transcript-level quantification of next-generation RNA-sequencing data from post-mortem anterior cingulate (ACC) and dorsolateral prefrontal cortices (DLPFC) of people with pathology-verified LBD (LBD = 14; Controls = 7) using Salmon. We identified differentially expressed transcripts (DET) using edgeR and investigated their functional implications using DAVID. We performed transcriptome-wide alternative splicing analysis using DRIMseq. We identified 74 DET in ACC and 96 DET in DLPFC after Benjamini-Hochberg false discovery rate (FDR) correction (5%). There were 135 and 98 FDR-corrected alternatively spliced genes in ACC and DLPFC of LBD brains, respectively. Identified DET may contribute to LBD pathology by altering DNA repair, apoptosis, neuroplasticity, protein phosphorylation, and regulation of RNA transcription. We confirm widespread alternative splicing and absence of chronic neuroinflammation in LBD brains. Transcript-level differential expression analysis can reveal specific DET that cannot be detected by gene-level expression analyses. Therapeutic and diagnostic biomarker potential of identified DET, especially those from TMEM18, MICB, MPO, and GABRB3, warrant further investigation. Future LBD blood-based biomarker studies should prioritise measuring the identified DET in small extracellular vesicles.

We determine the cohomology of the closed Drinfeld stratum of p-adic Deligne–Lusztig schemes of Coxeter type attached to arbitrary inner forms of unramified groups over a local non-archimedean field. We prove that the corresponding torus weight spaces are supported in exactly one cohomological degree and are pairwise non-isomorphic irreducible representations of the pro-unipotent radical of the corresponding parahoric subgroup. We also prove that all Moy–Prasad quotients of this stratum are maximal varieties, and we investigate the relation between the resulting representations and Kirillov’s orbit method.

The Critically Endangered Arabian leopard Panthera pardus nimr was believed to be absent from the Nejd region in Dhofar Governorate, Oman. However, a scat confirmed by DNA analysis in 2011 and camera-trap images from 2014 confirmed the presence of the leopard in this region. During 2014–2021, our camera traps documented at least eight individual leopards, demonstrating the species is resident and breeding in the region. This finding extends the Arabian leopard's known range in Oman by c. 40 km northwards. To improve detection probability, we recommend that camera-trap surveys for the leopard in the Arabian Peninsula are of at least 18 weeks duration. We advocate the designation of central and western areas of the Nejd as a National Nature Reserve, to protect critical habitat for the Arabian leopard and for other species in this region.

We provide a uniform bound on the partial sums of multiplicative functions under very general hypotheses. As an application, we give a nearly optimal estimate for the count of $n \le x$ for which the Alladi–Erdős function $A(n) = \sum_{p^k \parallel n} k p$ takes values in a given residue class modulo q, where q varies uniformly up to a fixed power of $\log x$. We establish a similar result for the equidistribution of the Euler totient function $\phi(n)$ among the coprime residues to the ‘correct’ moduli q that vary uniformly in a similar range and also quantify the failure of equidistribution of the values of $\phi(n)$ among the coprime residue classes to the ‘incorrect’ moduli.

The evolving global order and regional dynamics have profoundly impacted China-Southeast Asia relations. As the world grapples with the geopolitical implications of intensified US-China competition, the Association of Southeast Asian Nations countries find themselves navigating a complex interplay of opportunities and challenges. The US-led Indo-Pacific strategy has significantly reshaped the geopolitical landscape, yet Southeast Asia’s relations with China are marked by interwoven challenges and opportunities. This special issue includes six papers that cover Malaysia, Vietnam, Thailand, Indonesia, Cambodia, and the Philippines, illustrating how small and medium-sized states navigate an increasingly multipolar world. A central theme across the papers in this special issue is the critical role of domestic factors in shaping each country’s relationship with China.

The notion of Vasconcelos invariant, known in the literature as v-number, of a homogeneous ideal in a polynomial ring over a field was introduced in 2020 to study the asymptotic behavior of the minimum distance of projective Reed–Muller type codes. We initiate the study of this invariant for graded modules. Let R be a Noetherian $\mathbb {N}$-graded ring and M be a finitely generated graded R-module. The v-number $v(M)$ can be defined as the least possible degree of a homogeneous element x of M for which $(0:_Rx)$ is a prime ideal of R. For a homogeneous ideal I of R, we mainly prove that $v(I^nM)$ and $v(I^nM/I^{n+1}M)$ are eventually linear functions of n. In addition, if $(0:_M I)=0$, then $v(M/I^{n}M)$ is also eventually linear with the same leading coefficient as that of $v(I^nM/I^{n+1}M)$. These leading coefficients are described explicitly. The result on the linearity of $v(M/I^{n}M)$ considerably strengthens a recent result of Conca which was shown when R is a domain and $M=R$, and Ficarra–Sgroi where the polynomial case is treated.

A 1st-c. CE lamp from Cyprus, now in the Metropolitan Museum of Art, features a discus design of a satyr on a base before an enclosure. Formerly identified as a nude silenus, the design on this lamp and others with the same decoration in fact illustrates a motif after the Forum Marsyas statue from the Forum Romanum. The statue is typically understood as a symbol of civic libertas, and copies were erected in provincial fora and depicted on civic coinage in the 2nd and 3rd c. CE. This note argues that the lamps enhance our understanding of the Forum Marsyas in two respects. First, the lamps demonstrate that the motif was in provincial circulation ahead of the sculptural and numismatic trend. Second, it is now clear that the Forum Marsyas was used in private contexts, and potentially with a non-civic meaning, more extensively than previously understood. The lamps are therefore significant for understanding the provincial spread and legibility of this important but still enigmatic motif.

The triangle removal states that if G contains $\varepsilon n^2$ edge-disjoint triangles, then G contains $\delta (\varepsilon )n^3$ triangles. Unfortunately, there are no sensible bounds on the order of growth of $\delta (\varepsilon )$, and at any rate, it is known that $\delta (\varepsilon )$ is not polynomial in $\varepsilon $. Csaba recently obtained an asymmetric variant of the triangle removal, stating that if G contains $\varepsilon n^2$ edge-disjoint triangles, then G contains $2^{-\operatorname {\mathrm {poly}}(1/\varepsilon )}\cdot n^5$ copies of $C_5$. To this end, he devised a new variant of Szemerédi’s regularity lemma. We obtain the following results:

• • We first give a regularity-free proof of Csaba’s theorem, which improves the number of copies of $C_5$ to the optimal number $\operatorname {\mathrm {poly}}(\varepsilon )\cdot n^5$.

• • We say that H is $K_3$-abundant if every graph containing $\varepsilon n^2$ edge-disjoint triangles has $\operatorname {\mathrm {poly}}(\varepsilon )\cdot n^{\lvert V(H)\rvert }$ copies of H. It is easy to see that a $K_3$-abundant graph must be triangle-free and tripartite. Given our first result, it is natural to ask if all triangle-free tripartite graphs are $K_3$-abundant. Our second result is that assuming a well-known conjecture of Ruzsa in additive number theory, the answer to this question is negative.

Our proofs use a mix of combinatorial, number-theoretic, probabilistic and Ramsey-type arguments.

The influence of appetite and energy intake on energy compensation in response to chronic exercise remains poorly understood. This study examined the temporal impact of habitual exercise on energy intake and the homeostatic appetite regulators that influence energy compensation. Twelve-week-old male Sprague Dawley rats (n=30) fed an AIN-93M diet were randomised into 1 of 3 groups: 1) sedentary control (SED); 2) voluntary wheel exercise (EX); and 3) sedentary, weight-matched to aerobic exercise (SED-WM) for 8 weeks. Measures of energy intake, body weight, and adiposity were assessed. Appetite-regulating hormones acyl-ghrelin, active GLP-1, leptin, and insulin were measured in response to an oral glucose tolerance test. Rats with running wheels completed an average of 192kms over 8 weeks. While energy intake was initially reduced in EX, energy intake gradually increased with exercise training after week 1 (P<0.05). Body weight was lower in EX relative to SED from weeks 3-5, but did not differ at the end of the study. Fat mass and long-term satiety hormones leptin and insulin were lower in EX (P<0.05). No differences were observed in concentrations of the satiety hormone active GLP-1 or the orexigenic hormone acyl-ghrelin. Short-term homeostatic regulators of appetite do not appear to be altered with exercise training. The reduction in adiposity and associated decrease in tonic satiety hormones leptin and insulin are likely contributors to the coupling of energy expenditure with energy intake over time with voluntary exercise.

Safe and effective navigation of the world's oceans and waterways relies on maritime education and training. This involves the learning of motor, procedural and verbal components of complex skills. Motor learning theory evaluates training variables, such as instructions, feedback and scheduling, to determine best practices for long-term retention of such skills. Motor learning theory has come a long way from focusing primarily on underlying cognitive processes to now including individual and contextual characteristics in making predictions about instructional strategies and their role in performance and learning. A remaining challenge in applying recent motor learning theory to maritime education and training is a lack of empirical testing of complex vocational skills, such as simulation scenarios, with delayed retention and transfer tests. Incorporating theory-based understanding of beneficial instructional practices, through both cognitive approaches and those considering context and environment, task complexity and learner characteristics is a fruitful way forward in advancing maritime education and training.