Abstract: Prior work showed that human-in-the-loop oversight becomes structurally untenable in high-loss domains when AI output velocity V exceeds human cognitive capacity C_max. The operative constraint, however, is not V alone but V × L, where L denotes per-item cognitive load. L consists of triage, judgment, and response, which respond asymmetrically to AI capability improvement. Triage cost does not decline as models become more capable, because semantic indeterminacy is inherent in general-purpose design. Response cost is invariant to accuracy improvements. Only judgment cost faces downward pressure, and this pressure often operates by inducing omission rather than genuine reduction. Capability improvement therefore restructures L rather than reducing it. Governance mechanisms based on evaluating whether AI output is correct either delegate that evaluation to AI and inherit hallucination risk, or delegate it to humans and face the V × L ceiling. We propose Flow-by-Flow, a governance paradigm that controls supervisory load without evaluating content. A cognitive cost score based on formal, countable features imposes nonlinear costs on high-volume production, while an institutional capacity cap keeps processing volume within C_max. We derive four design invariants for any content-judgment-bypass exceedance pathway: no content judgment, no scalable consumption of examiner capacity, identity-bound per-application friction, and no batch clearance. One reference implementation is discussed to show that these invariants are jointly satisfiable, while its practical difficulties are explicitly acknowledged. An illustrative Monte Carlo analysis across 1,000 parameter draws suggests that composite multi-metric flow control outperforms supervision reinforcement alone in 90.8% of trials.

Abstract: Medical image segmentation under limited annotation budgets remains a critical challenge, particularly for anatomical structures exhibiting low-contrast boundaries—a pervasive problem in cardiac MRI, dermoscopy, and ultrasound imaging. Existing semi-supervised methods leverage consistency regularization and pseudo-label strategies but typically treat image preprocessing as a static pipeline step, failing to exploit the rich structural priors encoded in frequency-enhanced representations. In this paper, we propose FDPSeg, a novel Frequency-Domain Prior guided semi-supervised Segmentation framework that integrates Contrast-Limited Adaptive Histogram Equalization (CLAHE)-derived frequency priors directly into the transformer attention mechanism. Our dual-branch encoder processes both the original image and its CLAHE-enhanced counterpart, with a learned channel-attention fusion module that adaptively weights spatial and frequency features per image region. A novel frequency-domain consistency loss enforces structural coherence between teacher and student networks in the Fourier space, providing stronger supervisory signal for unlabeled data than spatial consistency alone. Experiments on the ACDC cardiac MRI dataset, the ISIC 2018 skin lesion dataset, and the BUSI breast ultrasound dataset demonstrate that FDPSeg consistently outperforms state-of-the-art semi-supervised baselines under 5% and 10% labeled data regimes, achieving improvements of up to 2.1% in mean Dice score and 3.8 mm reduction in 95th-percentile Hausdorff Distance (HD95) over the strongest competitor, with particularly pronounced gains on low-contrast boundary regions.

Abstract: Background: Intertumoral differences in glioblastoma (GBM) malignancy pose significant challenges for clinical management. Distinct microvascular growth patterns contribute substantially to tumor heterogeneity. Ultrasound localization microscopy (ULM) enables microscale mapping of microvascular network remodeling by tracking individual microbubble trajectories in vivo. This study evaluated whether ULM-derived microvascular heterogeneity metrics can facilitate histopathology-based stratification of GBM malignancy. Methods: An orthotopic glioblastoma model was established in 113 Sprague–Dawley rats, and ULM-derived heterogeneity parameters were extracted from tumor regions of interest. Spearman’s rank correlation coefficients were used to assess associations between microvascular heterogeneity metrics and histopathological indices. The Kruskal–Wallis H and Mann–Whitney U tests were used to compare metrics across different levels of microvascular maturity and cell proliferation. A decision tree–based diagnostic model was developed using ULM-derived microvascular features. Results: Microvascular heterogeneity was significantly negatively correlated with the vascular maturity index (p < 0.001) and positively correlated with the cell proliferation index (p < 0.001), supporting the biological and pathological relevance of ULM-derived heterogeneity metrics. Compared with transitional microvessels, mature microvessels exhibited significantly lower tortuosity (p = 0.002). Orientation variance, fractal dimension, connectivity, local thickness, and the spatial distribution index also tended to decrease but did not reach statistical significance (p = 0.074–0.529). In contrast, all corresponding metrics were significantly higher in immature microvessels (p ≤ 0.007). Compared with the low-proliferation group, all heterogeneity-related parameters were significantly higher in the high-proliferation group (p < 0.001). The decision-tree model based on microvascular heterogeneity demonstrated high performance at the sample level in predicting microvascular maturity and cell proliferation status, achieving accuracies of 90.29% (p = 0.029) and 92.23% (p = 0.026), respectively. Conclusions: We developed a clinically implementable decision-tree diagnostic model to support GBM malignancy stratification. As super-resolution ultrasound advances toward clinical translation, our findings may help inform future clinical decision-making.

Abstract: Background: Colorectal cancer (CRC) continues to be a leading cause of global oncology-related deaths. While mRNA vaccines delivered via lipid nanoparticles (LNPs) have achieved clinical success, challenges regarding systemic inflammatory potential, complex multi-step manufacturing, and cold-chain dependence persist. This study explores an alternative delivery paradigm using Nona-arginine (R9), a cell-penetrating peptide, to stabilise mRNA encoding the Carcinoembryonic Antigen (CEA), providing a biocompatible, LNP-free platform for CRC immunisation. Methods: CEA-encoded mRNA was synthesised through in vitro transcription and complexed with R9 at various Nitrogen-to-Phosphate (N/P) ratios. The resulting polyplexes were characterised using Dynamic Light Scattering (DLS) and Electrophoretic Mobility Shift Assays (EMSA). Molecular docking was employed to elucidate the structural stability of the carrier-cargo interface and the binding kinetics of vaccine-induced antibodies. The therapeutic index was validated in a CT26 murine colorectal tumour model (n=10/group), assessing tumour volume reduction, survival kinetics, and the density of tumour-infiltrating lymphocytes (TILs). Results: Optimal polyplex stability was achieved at an $N/P$ ratio of 10, yielding homogenous particles (142.5 ± 4.2 nm) with a protective zeta potential of +18.6 mV. In vivo evaluation demonstrated a 65% reduction in tumour burden and an $80\%$ survival rate in vaccinated cohorts compared to 0% in control groups. This clinical efficacy was correlated with a 3-fold increase in CD8+ T-cell infiltration, a 7.6-fold upregulation of Granzyme B, and the induction of high-affinity neutralising antibodies (∆∆G = -12.4 kcal/mol) targeting critical metastatic adhesion domains. Conclusion: The R9-mRNA platform serves as a highly effective, lipid-free alternative for CRC vaccination, eliciting a sophisticated "dual-strike" immune response. By bypassing the limitations of LNPs, this strategy offers a streamlined, stable, and potent pathway for the next generation of cancer immunotherapies.

Abstract: This article deals with sixth-degree polynomial equations and, more specifically, describes the necessary conditions under which the solutions of these polynomials can be expressed in closed-form radicals. For this purpose, eight different cases of sixth-degree polynomial equations will be discussed in detail. It is concluded that if a specific relation exists between the constant term and the remaining coefficients of a sixth-degree polynomial equation, then its solutions can be obtained by formulas expressed as functions of the initial coefficients and ultimately represented in terms of radicals. Each case of the polynomial discussed in this article is presented in the “problem–proof” format.

Abstract: Fine-grained action recognition in sports video anal- ysis presents a constellation of challenges that distinguish it from conventional human activity recognition tasks. When actions share substantial visual and temporal overlap—as is the case with cricket batting strokes—the discriminative cues necessary for accurate classification reside in subtle kinematic variations that operate at fine spatial and temporal granularities. This paper presents a comprehensive empirical investigation into the efficacy of contemporary temporal deep learning architectures for the classification of fifteen distinct cricket batting strokes using the CricShot10kdataset, a curated collection of approximately 10,000 video clips with balanced class representation. We conduct a rigorously controlled comparative evaluation of four distinct modeling paradigms: a non-temporal convolutional baseline em- ploying frame-averaged ResNet50 features, a unidirectional Long Short-Term Memory (LSTM) network, a bidirectional LSTM (BiLSTM) architecture, and a Transformer encoder with multi- head self-attention. All models are trained and evaluated under identical experimental conditions, including uniform frame sam- pling (32 frames per video), consistent spatial feature extraction (2048-dimensional ResNet50 embeddings), matched data splits, and standardized optimization hyperparameters. This method- ological rigor ensures that observed performance differences can be attributed cleanly to architectural choices in temporal modeling rather than confounding experimental variables. Our empirical results establish a clear performance hierarchy among the evaluated architectures. The BiLSTM model achieves the highest classification accuracy at 44.0 %, followed by the unidirec- tional LSTM at 42.0 %, the non-temporal baseline at 34.0 %, and notably, the Transformer architecture at only 23.0 %—a result that falls substantially below even the frame-averaged baseline. Statistical validation through McNemar’s test confirms that the 2 % improvement from LSTM to BiLSTM is highly significant (p < 0.001), indicating systematic correction of specific misclassi- fication patterns rather than random variation. Detailed per-class analysis and confusion matrix examination reveal pronounced performance heterogeneity across the fifteen stroke categories. High-performing classes such as the pull shot and cut shot exhibit F1-scores exceeding 0.65, attributable to their distinctive lateral motion patterns that create separable trajectories in the spatiotemporal feature space. Conversely, a cluster of front-foot strokes—including the cover drive, defensive shot, down-the- wicket stroke, and lofted offside drive—constitute the primary locus of classification error, with pairwise confusion rates frequently exceeding 40 %. We attribute these persistent confusions to the visual and temporal similarity of these strokes, which share common initial footwork, comparable bat trajectories through the downswing phase, and overlapping follow-through dynamics. The frame-level ResNet50 features, while capturing high-level spatial semantics effectively, lack the temporal granularity and explicit motion encoding necessary to resolve these fine-grained distinctions. Our error analysis further reveals that the model struggles to capture subtle kinematic cues such as bat face angle at impact, degree of wrist rotation, bat elevation trajectory, and the precise timing of weight transfer—features that human experts rely upon for stroke differentiation. The pronounced underperformance of the Transformer architecture provides a critical case study in the data efficiency limitations of attention- based models for fine-grained visual sequence tasks. Despite its theoretical capacity to model long-range dependencies without the sequential bottleneck of recurrence, the Transformer’s lack of built-in inductive biases regarding temporal locality and sequen- tial ordering renders it vulnerable to overfitting in moderate- data regimes. With approximately 400 training examples per class, the CricShot10kdataset provides insufficient statistical sig- nal for the Transformer to learn robust spatiotemporal atten- tion patterns from scratch, resulting in degraded generalization performance. This finding underscores an important principle for practitioners: architectural sophistication does not guarantee empirical superiority; rather, the choice of temporal modeling strategy must be carefully aligned with dataset scale and task characteristics. The contributions of this work are fourfold. First, we establish a rigorous and reproducible benchmark for cricket stroke classification on the CricShot10kdataset, providing a standardized reference point for future research. Second, through systematic architectural comparison, we quantify the marginal contribution of bidirectional temporal context to clas- sification performance and demonstrate its statistical significance. Third, we provide granular error analysis that identifies specific stroke categories and confusion pairs that dominate classification failures, thereby directing future research efforts toward the most impactful areas for improvement. Fourth, we offer a critical assessment of Transformer limitations in fine-grained, moderate-data video classification scenarios, contributing to the broader understanding of attention mechanism applicability. This paper is organized as follows. Section II reviews related work in action recognition, temporal modeling, and sports video analysis, situating our contribution within the broader research landscape. Section III details our methodological framework, including dataset characteristics, preprocessing pipelines, feature extraction protocols, and architectural specifications. Section IV presents comprehensive experimental results encompassing aggregate performance metrics, training dynamics, statistical validation, and per-class analysis. Section V provides extended discussion of key findings, interpreting the relative performance of architectures and analyzing the structure of classification errors. Section VI addresses limitations and outlines promising directions for future investigation. Section VII concludes with a summary of contributions and their implications for the field.

Abstract: Genetic recombination occurs in a wide range of organisms, from simple RNA viruses to mammals and plants with DNA genomes. In sexual reproduction, two parental genomes come together and undergo recombination, producing an offspring genome that has a combination of information from the two parental genomes. Genome recombination occurring during sexual reproduction can involve one of several mechanisms, including copy-choice recombination as well as breakage and exchange. Across widely different organisms, recombination by any mechanism is generally promoted by factors that damage the genetic material. In organisms such as bacteriophage and Paramecium, it was experimentally demonstrated that recombinational repair during sexual reproduction can overcome otherwise deleterious or lethal damages. For many decades it has been recognized that there are larger biological costs of sexual reproduction than for asexual reproduction. Much effort has been invested in theories assuming that genetic variation, due to recombination, is the main adaptive benefit of sexual reproduction. Such a benefit was considered to compensate for the large costs of sexual reproduction. However, it has been difficult to find a strong consistent benefit for variation. Repair of lethal damages, involving recombiantional interactions of two different genomes, now appears to be the major selective factor underlying sexual reproduction in organisms both simple and complex.

Abstract: Esca remains one of the most conceptually challenging disease syndromes of grapevine because it cannot be reduced to a single pathogen, lesion type or external phenotype. Foliar symptoms are erratic, internal wood damage is heterogeneous, and fungi associated with the syndrome may persist in asymptomatic vines. Much of this difficulty stems from treating esca-associated fungi as functionally equivalent, even though they occupy different niches and contribute differently to disease development. Here, we revisit grapevine esca through a fungal-biology-centred framework focused on Phaeomoniella chlamydospora, Phaeoacremonium minimumand white-rot basidiomycetes, especially Fomitiporia mediterranea. We argue that the esca pathosystem is best understood as the interaction between two biologically connected but non-equivalent fungal layers: a pioneer vascular phase and a later white-rot phase. Within this perspective, Petri disease and esca proper are interpreted as stages along a continuous host-fungus trajectory shaped by colonization strategy, tissue occupation, decay biology and pathobiome context. This distinction clarifies why host phenotypes are so difficult to interpret. Current evidence supports partially independent layers of host response, including resistance to pioneer colonization, tolerance to hydraulic dysfunction, resistance to wood decay and resilience under chronic infection. We therefore propose that “esca resistance” should be interpreted not as a unitary host trait, but as a multidimensional consequence of fungal functional differentiation, host physiology and environmental modulation.

Abstract:

Background/Objectives: We aimed to evaluate the efficacy and safety of trigonelline-rich Sakurajima radish on vascular endothelial function in patients with metabolic syndrome (MetS). Methods: In this multicenter, open-label, randomized, three-period crossover phase IIb trial, 21 patients with MetS were assigned to three 14-day sequences: Sakurajima radish powder, Aokubi radish powder, and a usual diet, separated by 14-day washouts. The primary outcome was flow-mediated dilation (FMD). The secondary outcomes included blood pressure (BP), urinary nitric oxide metabolites (NOx), and oxidative stress markers (8-hydroxy-2′-deoxyguanosine [8-OHdG]). Results: Twenty-one participants were included in this study. Sakurajima radish did not significantly improve FMD compared with the usual diet (control) (p = 0.58) or Aokubi radish (p=0.59). Unexpectedly, systolic BP was significantly higher with Sakurajima radish compared with control (+9.67 mmHg, p = 0.03) and Aokubi radish (+8.86 mmHg, p = 0.04). Urinary 8-OHdG/creatinine levels were also significantly higher with Sakurajima radish compared with control (p = 0.02), despite a significant elevation in urinary NOx levels (p = 0.03). A significant negative carryover effect on FMD was observed after the Aokubi radish period. Conclusions: Consumption of Sakurajima radish does not improve endothelial function in patients with MetS. Contrary to expectations, the intervention is associated with increased systolic BP and oxidative stress, despite elevated NOx levels. These findings suggest the need for caution regarding its cardiovascular application in patients with MetS.

Abstract:

Chloroplasts are the primary sites of photosynthesis, but growing evidence highlights their broader role as central hubs that coordinate plant responses to environmental challenges. They retain a semi-autonomous genetic system and communicate extensively with the nucleus through anterograde and retrograde signalling pathways, enabling coordinated cellular regulation. Beyond energy conversion, chloroplasts host key biosynthetic pathways and dynamically adjust their metabolic and redox states in response to developmental and environmental cues. This review summarizes current knowledge of chloroplast functions in responses to abiotic and biotic stress, emphasizing their contribution to plant resilience, productivity and sustainability. Under abiotic stress, chloroplasts undergo structural, metabolic and redox reprogramming to maintain photosynthetic efficiency and metabolic homeostasis. During biotic stress, they act as a powerful signalling platforms that integrate immune responses with metabolic and redox regulation. These functions rely on overlapping signalling pathways that are differentially tuned to support acclimation or defence. By coordinating stress responses with photosynthetic activity and metabolic efficiency, chloroplasts play a central role in sustaining plant productivity and represent promising targets to enhance crop resilience and agricultural sustainability under climate change and increasing pathogen pressure.

Abstract: This article investigates sensor placement strategies for three-dimensional (3-D) time-of arrival (TOA)-based target localization in Underwater Acoustic Sensor Networks (UASNs). To mitigate underestimation of localization accuracy in complex marine environments, the actual acoustic ray propagation time is derived, and the TOA measurement variance is estimated using the ray acoustic propagation model. These formulations enable a novel 3-D TOA measurement model, and the trace of Cramér-Rao lower bound (CRLB) for this model serves as the optimization criterion for sensor placement. The MinMax k-Means algorithm is proposed to determine the optimal sensor placement by minimizing the average of the trace of CRLB. Extensive numerical simulations are conducted to demonstrate the effectiveness of the placement strategies.

Abstract: This systematic literature review examines the long-standing problem of the tragedy of the commons within the field of public administration. Through a synthetic evaluation of institutional diagnostic and organizational analysis tools, this study deconstructs the traditional dichotomy between centralized state control and local self-governance. The findings reveal a critical interpretive gap: the lack of a coherent theoretical framework for the active, architectural role of the state. To fill this gap, the article develops a synthetic conceptual framework that redefines public administration not as a direct manager or an absent observer, but as an architect of multilevel, polycentric governance systems. This role involves providing institutional support, ensuring access to reliable information, managing cross-scale linkages, and guaranteeing conflict resolution. This approach shifts the focus from a search for a single solution toward the design of resilient institutional ecologies.

Abstract: Using a database of global total fertility rates (TFR) from 1990 to 2024, supplemented by a series of indicators, we can observe trends and explain them through cultural and socio-economic factors. Worldwide TFR dynamics show a clear distinction: low fertility (below replacement) in much of Europe, North America, and East Asia; high fertility in sub-Saharan Africa; and moderate fertility in countries at various stages of the demographic transition. Observed variations are explained by economic and social-determinants:GDP and Human Development Index are negatively correlated with TFR; high infant mortality rates correlate positively with TFR; and greater contraceptive prevalence and higher average maternal age at birth are associated with fertility declines. Cultural factors – such as dominant religion or official demographic policies – can modify overall trends, and the level of democratic freedom influences access to reproductive health information and services. These disparities reflect structural differences in socio-economic development, public health, gender equality and social policy.

Abstract: Background: The transverse view of the thyroid gland is routinely obtained in clinical ultrasound. However, no specific sonographic sign is yet available to indicate that the scanned plane approximates the transverse section that fully displays the isthmus. Observation: We propose the “Arch Bridge Sign” as a novel sonographic sign for a scanned plane that approximates the transverse section of the thyroid gland while fully displaying the isthmus. The sign is defined by three key features: (1) bilateral lobes that appear symmetric, (2) isthmus is clearly visualized, and (3) isthmus appears as a smooth arched curvature (the “arch”) connecting two lateral lobes (the “piers”), together resembling an arch bridge. Conclusion: The “Arch Bridge Sign” provides a simple, intuitive sonographic sign for identifying a scanned plane that approximates the transverse section fully displaying the isthmus. It may serve as a practical reference for scanning quality control and a useful teaching tool for trainees.

Abstract: Non-alcoholic fatty liver disease (NAFLD) specifically includes the stage of simple fatty liver and the stage of hepatitis. In the late stage of the disease, it resembles the early stage of cirrhosis. Mesenchymal stem cells regulate metabolic pathways and energy transport pathways in disease models, reducing the synthesis and utilization of glucose and fatty acids, and restoring the homeostasis of the internal microenvironment. For areas with more severe damage, umbilical cord mesenchymal stem cells (UCMSC) are used for regenerative repair. Mesenchymal stem cells release exosomes in a paracrine manner into the damaged areas of the liver, promoting the differentiation and development of hepatic progenitor cells into hepatocytes, reducing differentiation into cholangiocytes, while assisting hepatic progenitor cells in resisting the progression of inflammation and fibrosis, and promoting the normal function of adaptive immune responses.

Abstract: Malaria and coronavirus disease-2019 (COVID-19) may have similar aspects and seem to have a strong potential for mutual influence. They have already caused millions of deaths, and regions where malaria is endemic are at risk of further suffering from the consequences of COVID-19 due to mutual side effects, like less access to treatment due to fear of access to health facilities leading to diagnostic delays and worse outcomes. A narrative literature review was conducted by searching online databases like Pub Med, Cochran, Medline, Google scholar, malarial journals, health journals, MDPI and biomed central related journals, 133 articles published from 2004 to 2024 were analysed and discussed. The Management of malaria during the COVID-19 pandemic in Uganda required a comprehensive approach that balances the need for both malaria and COVID-19 control, prevention and treatment. These include: Integration of services, healthcare infrastructure strengthening, expanded testing, treatment access, community education and awareness, health worker training, testing and surveillance, mobile health solutions, community engagement, research and innovation, adaptive management, cross-sector collaboration, international cooperation, vector control, monitoring and evaluation. In this chapter, we provide a comprehensive review of integrated management approaches for malaria and covid-19 management in Uganda. In implementing this comprehensive approaches, we can effectively manage both malaria and COVID-19, reduce the burden of disease, and protect the health and well-being of communities in Uganda and worldwide.

Abstract: Guizhou Province, a typical karst mountainous region in southwest China, features a complex geographical environment and diverse ethnic cultures, which together have fostered unique traditional village landscapes. Taking 757 national and provincial-level ethnic traditional villages in Guizhou as the research object, this study employs methods including GIS spatial analysis, the nearest neighbor index, and kernel density estimation to quantitatively reveal the geographical distribution characteristics, spatial differentiation patterns, and underlying causes of Miao, Dong, Bouyei, and Han Tunpu villages from the perspectives of two core physical geographic factors: topography and river systems. The results show that: (1)In terms of topographic distribution, village sites exhibit a significant vertical differentiation pattern: the Miao people "reside in the mountains", the Dong and Bouyei people "stay close to water", and the Han Tunpu settlements "occupy strategic passages". Meanwhile, a slight preference for sunny slopes is observed (52.4% of villages are on sunny slopes), but no overwhelming "sun-seeking, shade-avoiding" tendency exists. (2)Regarding river system distribution, different ethnic groups display distinct patterns of water utilization: the Dong and Bouyei people form a tight "ribbon along rivers" dependency (over 70% of villages are within 1 km of a river), the Miao people rely on mountain streams with a pattern of "far from large rivers, close to small ones", and the Han Tunpu settlements adopt an "engineered" transformation and utilization pattern. (3)Quantitative analysis shows that the spatial distribution of villages is significantly clustered, forming three high-density core areas: the Duliu River, Qingshui River, and Tunpu areas. Elevation, slope gradient, and distance to rivers are key natural constraint factors. This study reveals a "non-random" three-dimensional distribution pattern of ethnic traditional villages in Guizhou, which represents an optimal spatial response of various ethnic groups to the complex karst environment based on their historical migration memories, livelihood strategies, and cultural adaptability. This finding is of great value for understanding the mechanism of ethnic-environment interaction and for the conservation of traditional villages.

Abstract: In this paper, we consider the classes of generalized Stampacchia mixed weak vector variational-hemivariational inequalities (in short, GSMWVVHI) and generalized Minty mixed weak vector variational-hemivariational inequalities (in short, GMMWVVHI), formulated in terms of bifunctions. By employing the Knaster-Kuratowski-Mazurkiewicz-Fan (in short, KKM-Fan) lemma, we deduce an existence result for the solutions of GSMWVVHI without imposing any monotonicity assumptions on bifunctions and relaxed compactness hypotheses. Moreover, under generalized stable pseudomonotonicity hypotheses on bifunctions, we derive an existence theorem for the solutions of GMMWVVHI and establish an equivalence relation between the solutions of GSMWVVHI and GMMWVVHI. Furthermore, uniqueness results for the solutions of GSMWVVHI and GMMWVVHI are established under suitable assumptions. Several illustrative examples have been furnished to highlight the applicability and relevance of the established results. To the best of our knowledge, existence and uniqueness results for solutions of GSMWVVHI and GMMWVVHI have been established for the first time in this paper on the Euclidean spaces.

Abstract:

We provide a coordinate-free characterisation of phase boundaries in field theory by proving that a complex scalar field on a globally hyperbolic spacetime with boundary admits a stratified covariant phase space. The stratification is governed by a diffeomorphism-invariant functional $P$ partitioning spacetime into strata, together with a finite-energy selection rule: in the dense stratum $\{P \geq P_\star\}$, a diverging phase-stiffness functional $\kappa(P)$ forces any finite-action tangent vector to satisfy $\delta\theta = 0$, reducing the admissible variation class to amplitude fluctuations alone. We show that this selection rule simultaneously enlarges the presymplectic kernel of the augmented symplectic form $\Omega^{\mathrm{aug}}_\Sigma$ and suppresses the central extension of the boundary charge algebra: $K_{dens} = 0$. The Phase Boundary Characterisation Theorem establishes that these two effects are algebraically equivalent, identifying $\mathcal{H}$ as the unique degeneracy locus of $\Omega^{\mathrm{aug}}_\Sigma$ --- a purely coordinate-free characterisation independent of the specific trigger functional. The Iyer--Wald--Zoupas ambiguity in the boundary symplectic density is resolved by explicit mixed boundary conditions, and the algebraic structure on each stratum is compatible with standard quantization procedures applied independently per stratum.

Abstract: Background/Objectives: Induction of anti-SARS-CoV-2 antibodies by COVID-19 vaccination reduces morbidity and mortality, but immune responses may be compromised in people living with HIV (PLWH). The aims of the current study were to determine whether viral suppression (VS) or immune reconstitution (IR) in PLWH directly affected their ability to produce effective levels of anti-SARS-CoV-2 antibodies in mucosal secretions or blood induced by vaccination. Methods: Anti-SARS-CoV-2 spike IgG, IgA and secretory IgA (SIgA) antibodies and their avidities were measured by ELISA in HIV-negative healthy controls (HC; n=49) and PLWH (n=94) using stimulated oral fluid (SOF) and serum. Frequencies of CD4/CD8 T cells and their expression of exhaustion/senescence were determined by flow cytometry. Cytokine levels were measured by cytokine bead arrays. Results: We showed that higher HIV burden negatively impacted the levels of systemic and mucosal anti-SARS-CoV-2 spike IgG antibodies produced. This differential IgG antibody production was unaffected by the IR status, antiretroviral therapy duration or by T cell exhaustion/senescence. PLWH elicited higher anti-SARS-CoV-2 spike IgA antibodies both in peripheral blood and oral mucosa, and secretory IgA (SIgA) antibodies in the oral mucosa. PLWH with higher HIV burdens elicited lower IgG avidity but the IgA avidity indices remained unaffected. PLWH expressed higher levels of innate immunity cytokines irrespective of the HIV burden in the oral mucosa. Conclusions: Significantly fewer breakthrough infections in PLWH compared with HC, along with high IgA/SIgA antibodies and increased innate immunity cytokines in the SOF suggests a potential role for mucosal immunity in the immunopathogenesis of COVID-19.