A man in his 60s with multiple vascular comorbidities presented with sudden, painless vision loss in one eye. Although he had a high risk for atherosclerotic events, initial evaluation for stroke was negative for acute ischemia, but found to have markedly elevated inflammatory markers. Accordingly, giant cell arteritis was investigated and Ophthalmologic findings and fulfillment of the 2022 American College of Rheumatology/European Alliance of Associations for Rheumatology classification criteria supported the diagnosis of giant cell arteritis, despite a negative temporal artery biopsy. Management included high-dose glucocorticoids and delayed tocilizumab initiation due to the need for multiple vascular surgeries. Vision loss was irreversible, but systemic symptoms resolved and vascular interventions were successful. This case highlights the diagnostic and management complexities of biopsy-negative giant cell arteritis in patients with severe atherosclerotic vascular disease, emphasizing the importance of clinical judgment and established classification criteria when imaging and biopsy results are inconclusive.

A residual-set framework is introduced for analyzing additive prime conjectures, with particular emphasis on the Strong Goldbach Conjecture (SGC). For each even integer $E_n\ge 4$, the residual set $ℛ\left(E_n\right)=\{E_n-p\mid$ $p<E_n,p\in \mathbb{P}\}$ is defined, and the universal residual set ${ℛ}_{\mathbb{E}}={{{\displaystyle \cup }}^{\text{}}}_{E_n}ℛ\left(E_n\right)$ is constructed. It is shown that ${ℛ}_{\mathbb{E}}$ contains infinitely many primes. A nontrivial constructive lower bound is derived, establishing that the number of Goldbach partitions satisfies $G\left(E\right)\ge 2$ for all $E\ge 8$, and that the cumulative partition count satisfies ${\displaystyle \sum }_{E\le N}G\left(E\right)\gg \frac{N^2}{{\text{log}}^{4}N}$. An optimized deterministic algorithm is implemented to verify the SGC for even integers up to 16,000 digits. Each computed partition $E_n=p+q$ is validated using elliptic curve primality testing, and no exceptions are observed. Runtime variability observed in the empirical tests corresponds with known fluctuations in prime density and modular residue distribution. A recursive construction is formulated for generating Goldbach partitions, using residual descent and leveraging properties of the residual sets. The method extends naturally to Lemoine's Conjecture, asserting that every odd integer $n\ge 7$ can be expressed as $n=p+2q$, where $p,q\in \mathbb{P}$. A corresponding residual formulation is developed, and it is proven that at least two valid partitions exist for all $n\ge 9$. Comparative analysis with the Hardy-Littlewood and Chen estimates is provided to contextualize the cumulative growth rate. The residual-set methodology offers a deterministic, scalable, and structurally grounded approach to additive problems in prime number theory, supported by both theoretical results and large-scale computational evidence.

Background: Proper umbilical cord care prevents neonatal infections and reduces neonatal mortality. Despite global recommendations for evidence-based cord care practices, traditional beliefs, and inadequate maternal knowledge often lead to unsafe practices, particularly in low-resource settings like Bangladesh. This study aimed to assess the understanding of umbilical cord care among mothers of neonates in Sherpur District, Bangladesh, and identify factors associated with knowledge levels. Methods: A descriptive cross-sectional study was conducted from July to October 2020 at Sherpur Sadar Hospital. A total of 193 mothers of neonates were recruited using a non-randomized purposive sampling method. Data was collected through a pre-tested, semi-structured, interviewer-administered questionnaire. Knowledge levels were categorized as "Good" (>6) or "Poor" (≤6) based on responses to 10 structured questions. Statistical analyses, including chi-square tests and crude odds ratios (COR), were performed to identify socio-demographic factors associated with knowledge levels. Results: Of the 193 participants, 48.7% demonstrated "Good" knowledge, while 51.3% had "Poor" knowledge. Education level (p = 0.01), occupation (p = 0.02), family type (p < 0.001), and family size (p = 0.04) were significantly associated with knowledge levels. Mothers with higher education and those from joint families exhibited better knowledge. However, 28.5% of respondents were unaware of the typical umbilical cord-shedding timeframe, and 44% could not identify signs of infection. Unsafe practices, such as using medications (14.5%) or hot compression (7.2%) for drying the cord, were reported. Conclusion: The study reveals significant gaps in maternal knowledge regarding umbilical cord care in Sherpur District, driven by socio-demographic disparities and cultural practices. Targeted health education programs, emphasizing evidence-based cord care practices and leveraging local social structures, are urgently needed to improve neonatal health outcomes in similar resource-limited settings. Future research should evaluate the effectiveness of these interventions to inform policy and practice.

The integration of LiDAR and Artificial Intelligence (AI) has revolutionized feature detection in urban environments. LiDAR systems, which utilize pulsed laser emissions and reflection measurements, produce detailed 3D maps of urban landscapes. When combined with AI, this data enables accurate identification of urban features such as buildings, green spaces, and infrastructure. This synergy is crucial for enhancing urban development, environmental monitoring, and advancing smart city governance. LiDAR, known for its high-resolution 3D data capture capabilities, paired with AI, particularly deep learning algorithms, facilitates advanced analysis and interpretation of urban areas. This combination supports precise mapping, real-time monitoring, and predictive modeling of urban growth and infrastructure. For instance, AI can process LiDAR data to identify patterns and anomalies, aiding in traffic management, environmental oversight, and infrastructure maintenance. These advancements not only improve urban living conditions but also contribute to sustainable development by optimizing resource use and reducing environmental impacts. Furthermore, AI-enhanced LiDAR is pivotal in advancing autonomous navigation and sophisticated spatial analysis, marking a significant step forward in urban management and evaluation. The reviewed paper highlights the geometric properties of LiDAR data, derived from spatial point positioning, and underscores the effectiveness of machine learning algorithms in object extraction from point clouds. The study also covers concepts related to LiDAR imaging, feature selection methods, and the identification of outliers in LiDAR point clouds. Findings demonstrate that AI algorithms, especially deep learning models, excel in analyzing high-resolution 3D LiDAR data for accurate urban feature identification and classification. These models leverage extensive datasets to detect patterns and anomalies, improving the detection of buildings, roads, vegetation, and other elements. Automating feature extraction with AI minimizes the need for manual analysis, thereby enhancing urban planning and management efficiency. Additionally, AI methods continually improve with more data, leading to increasingly precise feature detection. The results indicate that the pulse emitted by continuous wave LiDAR sensors changes when encountering obstacles, causing discrepancies in measured physical parameters.