Abstract: Drug-related criminal activities on social media increasingly employ dynamic coded language—such as fruit substitutions, numeric homophones, and dialectal metaphors—to evade detection. This linguistic obfuscation poses significant challenges to conventional keyword-based monitoring systems. Furthermore, the scarcity of open-source datasets capturing these specific evasive expressions severely impedes automated detection research. To address these limitations, we construct a dedicated dataset of 10000 samples of drug-related coded texts sourced from mainstream Chinese social media platforms. Concurrently, we propose an optimized, TextCNN-based deep learning framework tailored for the automated identification of such illicit content. By leveraging multi-scale convolutional feature extraction, our model effectively captures intricate local semantic patterns and morphological variations inherent in short, highly noisy social media texts. Experimental results demonstrate that the proposed method achieves an F1-score of 99.3%, significantly outperforming established baseline approaches in the semantic representation of coded language. These findings indicate that our framework provides an efficient, robust, and scalable computational solution for intelligent drug-related content monitoring in complex online environments.

Abstract: Autonomous driving systems rely on a sophisticated pipeline of artificial intelligence models to perceive, predict, and plan in dynamic environments. This review presents a systematic analysis of the machine learning and deep learning models underpinning vehicle autonomy, spanning classical convolutional neural networks (CNNs) for object detection and semantic segmentation, to recurrent and Transformer-based architectures for trajectory prediction and motion planning. In this review, a critical examination of the autonomous vehicle sensor stack—including cameras, LiDAR, radar, ultrasonics, and GNSS/IMU as data acquisition systems, highlighting modality-specific AI challenges such as monocular depth estimation, 3D point cloud processing, and radar Doppler interpretation. The evolution of perception and decision-making pipelines is reviewed, contrasting modular architectures with end-to-end learning paradigms that directly map raw sensor data to control commands, and discussing their trade-offs in interpretability, safety assurance, and robustness to rare edge cases. We further survey specialized hardware accelerators and heterogeneous automotive SoCs designed to meet stringent real-time and power constraints. Industrial strategies are compared, including multi-modal sensor fusion and vision-centric approaches based on large-scale imitation learning. Finally, we identify open challenges related to robustness under adverse conditions, domain shift, causal ambiguity, and the need for interpretable and certifiable AI in safety-critical autonomous driving systems.

Abstract: Ultraweak photon emission (UPE) refers to spontaneous, low-intensity photon release from biological systems, generated largely through oxidative metabolic reactions involving reactive oxygen species, lipid peroxidation, mitochondrial activity, and electronically excited molecular intermediates. Because the nervous system is highly metabolically active and vulnerable to oxidative stress, hypoxia, excitotoxicity, inflammation, and mitochondrial dysfunction, UPE may offer a noninvasive optical window into neural physiology and disease. In this narrative review, we examine experimental and translational evidence linking UPE to nervous system function, with emphasis on neuronal excitation, glutamate-mediated activity, ischemia-reperfusion injury, stroke, neurodegeneration, mental-state and anesthesia paradigms, photobiomodulation, demyelinating disease, Parkinson disease, amyotrophic lateral sclerosis, and neuro-oncology. Across these domains, UPE appears most consistently associated with redox metabolism, mitochondrial function, oxidative stress, and excitation–metabolism coupling, whereas evidence that endogenous photons mediate functional neural signaling remains preliminary. Current data suggest that UPE may be most promising as a preclinical biomarker of tissue metabolic state, delayed post-ischemic dysfunction, and early neurodegenerative change, particularly when integrated with electrophysiology, perfusion imaging, molecular assays, and other physiologic measures. However, clinical translation is limited by low photon flux, limited temporal and spectral resolution, difficulty localizing signals from deep tissue, heterogeneous experimental protocols, and incomplete source attribution. Overall, UPE represents a promising but still early-stage framework for studying nervous system metabolism and disease, with future progress dependent on standardized methods, multimodal validation, and disease-specific investigation.

Abstract: Alzheimer’s disease (AD) is a progressive neurodegenerative disorder for which early and accurate diagnosis remains a critical challenge. In this work, we propose a Multi-ROI Multimodal 3D Vision Transformer for AD classification that integrates structural MRI data with clinical and volumetric biomarkers within a unified attention-based framework. The proposed approach leverages anatomically guided multi-region-of-interest (ROI) decomposition to focus on disease-relevant brain structures, including the hippocampus, entorhinal cortex, fornix, and major cortical lobes. Each ROI is encoded using 3D tubelet embeddings, while clinical and volumetric features are transformed into feature-wise tokens, enabling seamless multimodal fusion through self-attention mechanisms. A hemisphere-aware selection strategy is introduced to identify the most discriminative ROI representations, enhancing both performance and interpretability. The model is evaluated on a merged multi-cohort dataset combining ADNI, AIBL, and OASIS, using a 7-fold cross-validation protocol. Experimental results demonstrate that the proposed method achieves high classification performance, reaching an accuracy of 97.62% and an AUC of 0.9940, outperforming single-modality and whole-brain baselines. Furthermore, attention-based analysis provides interpretable insights into the relative importance of clinical and neuroanatomical features, revealing consistency with established AD biomarkers. These findings highlight the effectiveness of multimodal integration and ROI-based representation for robust and explainable AD classification.

Abstract: Background and Objectives: Vitamin D deficiency is a pervasive public health issue in high-latitude regions, yet large-scale population data for the Baltic states remain sparse. This study aimed to determine the prevalence of vitamin D status and identify its primary determinants within a primary care setting in Lithuania. Materials and Methods: We conducted a retrospective cross-sectional analysis of serum 25-hydroxyvitamin D [25(OH)D] concentrations from 14,330 unique patients (aged 1–101 years) collected during 2025 at a major clinic in Vilnius. Vitamin D status was categorized according to the Central and Eastern European Expert Consensus thresholds. Results: The overall median 25(OH)D concentration was 68.3 nmol/L (Mean: 74.7 nmol/L; SD: 35.1), placing the population average in the "insufficiency" range (50–75 nmol/L). Seasonality emerged as the most significant predictor of deficiency; multivariable logistic regression showed a maximal risk reduction in September (OR 0.33; 95% CI: 0.27–0.41) and August (OR 0.34) compared to January, while June and November provided no significant protection. Age-specific analysis revealed a non-linear "U-shaped" distribution: children aged 0–6 years had the highest levels (mean ~100 nmol/L), likely due to rickets prophylaxis, whereas adolescents (12–18 years) exhibited the highest vulnerability, with approximately 80% suffering from deficiency or insufficiency. Males faced a 13.9% higher likelihood of deficiency than females (OR 1.14; p = 0.0036), potentially due to lower rates of elective supplementation. Conclusions: These findings suggest that current supplementation strategies successfully protect infants but fail to sustain adequacy through adolescence and adulthood, particularly during the "vitamin D winter." Targeted public health interventions for adolescents and year-round monitoring are recommended to mitigate the high prevalence of suboptimal vitamin D status in Lithuania.

Abstract: The association of small molecules with lipid membranes plays a central role in drug delivery, pharmacokinetics, toxicity, and membrane biophysics, also being of fundamental importance in drug pharmacodynamics given that most drug targets are membrane-associated proteins. Accurate determination of solute–membrane association affinities, however, remains challenging due to the diversity of experimental systems, the complexity of membrane environments, and the intrinsic limitations of individual methodologies. This review provides a comprehensive overview of the experimental and computational approaches currently used to quantify small molecules association with lipid membranes. Standard experimental techniques, including spectroscopy-based methods, calorimetry, electrophoretic measurements, and surface-sensitive approaches, are discussed alongside established computational strategies ranging from continuum models to atomistic molecular dynamics simulations. Particular emphasis is placed on the formalisms required for data analysis, including partitioning models and thermodynamic frameworks, as well as on the assumptions underlying each method. The validity limits, sources of uncertainty, and common experimental and interpretative pitfalls are critically examined. By providing a unified and comparative perspective, this work establishes a structured framework for the quantitative study of solute–membrane interactions, guiding new researchers in the selection of appropriate methodologies and in the rigorous analysis of experimental and computational results. Moreover, it enables the consistent and quantitative rationalization of affinity parameters reported across the literature, supporting the development of curated datasets and predictive relationships that can inform the design of new and more effective drugs.

Abstract: Aluminium powder, an energetic material, is prone to thermal runaway upon water exposure under local heat sources, yet the nonadiabatic mechanisms of micron sized accumulated aluminium powder under localized heating remain unclear. This study employs a proprietary characterization platform to investigate the effects of particle size, water content, and local heat source power on heat transfer in the dry state and on parameters including induction time, onset temperature, peak heat release rate, and reaction heat during the induction and main reaction phases. In the dry state, decreasing particle size enhances effective thermal conductivity and accelerates temperature rise, whereas elevated local heat source power exacerbates thermal inertia. Under local heating upon water exposure, reduced particle size significantly enhances reactivity; the reaction heat of 2 μm powder reaches 983 J/g, approximately fourfoldAs shown in Figure9 that of 106 μm powder. Water content exhibits nonmonotonic regulation, with onset temperature minimizing at 25% water content and 66.4 °C and reaction heat peaking at 33%. Paradoxically, elevated local heat source power suppresses reaction intensity, and reaction heat at 10 W is one sixth of that at 2.5 W, attributed to rapid product layer densification and the steam film barrier effect shifting the controlling mechanism from chemical to diffusion control. A coupled multifactorial predictive model incorporating the three factors was established with R2 of 0.92, providing data and guidance for aluminium powder storage hazard prevention.

Abstract: Binary sequences (binary codes), where the elements are −1 or +1, are useful in many fields, including communications, radar, sonar, mathematics, physics, and cryptography. This paper considers binary sequences with low aperiodic autocorrelations and focuses on the small peak sidelobe levels alongside the merit factor. Two families of binary sequences are considered, namely Rudin-Shapiro and Legendre sequences. For both families, we applied a heuristic algorithm to minimize the peak sidelobe levels for sequences of lengths up to 2^16 and 220−1, respectively. The main contribution of the article is two conjectures associated with Legendre sequences: (1) The obtained binary sequences with the best-known peak sidelobe levels have merit factor ≈5.0, (2) The number of elements that differ between the resulting binary sequences and the initial Legendre sequences follows a linear dependence on the sequence length (n), namely ≈0.01n. The Rudin-Shapiro sequences do not exhibit these properties, as worse peak sidelobe level and merit factor values were obtained. The number of elements that differ between the resulting binary sequences and the initial Rudin-Shapiro sequences is also much higher compared to that of the Legendre sequences.

Abstract: Existence of global smooth solutions to the three-dimensional (3D) Navier-Stokes equations is disproved for pressure-driven plane Poiseuille flow with no-slip boundary conditions. This study is rigorously grounded in Sobolev space analysis. We show that the solution breakdown arises from the regularity degeneration instead of velocity blow-up. For disturbed laminar plane Poiseuille flow, the instantaneous velocity field is decomposed into a time-averaged flow and a disturbance flow, both characterized by their regularity in Sobolev spaces. When the Reynolds number is larger than the critical Reynolds number, the nonlinear interaction modifies the mean flow profile, and the disturbance amplitude grows significantly. This amplification leads to a local cancellation between viscous terms of the mean flow and the disturbance flow, resulting in the total viscous term (i.e., the Laplacian term) vanishing locally at the critical point $(\boldsymbol{x}^*, t^*)$. The local vanishing viscous term leads to zero velocity according to the Energy-Velocity Monotonicity Principle (EVMP), which contradicts the non-vanishing incoming velocity, leading to formation of a singularity. This singularity induces a velocity discontinuity, which causes the $L^\infty$ -norm of the velocity gradient to diverge, violating the definition of a global smooth solution in Sobolev spaces. The analysis is strictly grounded in partial differential equations (PDE) theory, with all key steps validated by Sobolev space properties and a priori estimates.

Abstract: Persistent post-concussion symptoms (PPCS) following mild traumatic brain injury (mTBI) are common and frequently disabling. However, symptom persistence is often poorly correlated with injury severity or structural brain abnormalities. Increasing clinical and research evidence suggests substantial overlap between PPCS and functional neurological disorder (FND), yet this interface remains poorly synthesised and conceptually unresolved. To systematically review and synthesise the evidence linking mTBI with functional neurological symptoms, and to refine existing conceptual models by proposing a clinically useful framework for differentiating functional and organic contributions to persistent post-concussion presentations. A scoping review with narrative synthesis were conducted. Database searches yielded 120 records; after duplicate removal and abstract screening, 32 studies underwent full-text review. Included studies comprised systematic reviews, narrative and conceptual reviews, mechanistic hypothesis papers, primary observational studies, case series, case reports, and early interventional and neu-roimaging investigations examining functional neurological symptoms in the context of mTBI. The literature demonstrates substantial phenomenological overlap between PPCS and FND across cognitive, motor, sensory, visual, and seizure-related domains. Functional neurological symptoms can emerge after concussion and may closely resemble PPCS, often in association with psychiatric comorbidity, dissociation, trauma exposure, and maladaptive attentional or illness-belief processes. Objective neurological impairment and injury severity show weak and inconsistent associations with symptom persistence. The evidence base is dominated by clinic-derived observational studies, with no population-level incidence estimates identified. Functional neurological symptoms represent a significant and under-recognised contributor to persistent symptoms after mTBI. Existing evidence supports moving beyond binary organic–psychogenic models toward a functional–organic differentiation framework that acknowledges dynamic interactions between injury-related and functional mechanisms. Improved screening, diagnostic communication, and stratified management are likely to enhance outcomes for patients with persistent post-concussion symptoms.

Abstract: Background: Transradial access has become a preferred strategy for chronic total occlusion (CTO) percutaneous coronary intervention (PCI) because of lower access-site complication rates and increasing feasibility for complex CTO techniques using large-bore slender or sheathless systems. However, long-term outcomes after successful transradial CTO recanalization and their predictors remain incompletely defined. We aimed to identify long-term clinical and procedural predictors of major adverse cerebrovascular and cardiac events (MACCE) after successful transradial CTO PCI. Methods: We performed a prospective dual-center cohort study including 227 consecutive patients who underwent successful transradial CTO PCI at two high-volume catheterization laboratories with dedicated CTO programs. A total of 405 CTO PCI procedures were screened; all femoral-access cases were excluded and only transradial cases were eligible. Baseline clinical characteristics, left ventricular ejection fraction (LVEF), lesion complexity including J-CTO score, coronary disease extent, and procedural variables were prospectively collected and/or verified from institutional databases. The primary endpoint was MACCE, defined as a composite of all-cause death, non-fatal myocardial infarction, target vessel revascularization, and stroke/transient ischemic attack. Event rates were estimated using Kaplan-Meier methods. Predictors were explored using Cox proportional hazards regression with clinically relevant covariates and procedural characteristics entered into multivariable models. Results: Among 227 patients with successful transradial CTO recanalization and complete 5-year follow-up among survivors, cumulative MACCE and all-cause mortality were 44.0% and 21.5%, respectively. In multivariable Cox analysis, prior myocardial infarction, right coronary artery target vessel, and a higher number of implanted stents were independently associated with increased MACCE risk, whereas previous PCI and preserved LVEF (≥40%) were associated with lower MACCE risk. For all-cause mortality, preserved LVEF was independently protective, while right coronary artery target vessel intervention was associated with increased mortality risk; severe chronic kidney disease showed a significant univariable association and remained a strong signal after multivariable adjustment. Conclusions: After successful transradial CTO PCI, long-term MACCE appears to be driven primarily by baseline comorbidity and coronary disease burden rather than by access-related factors. Integrating clinical risk markers with anatomic and procedural markers may improve long-term prognostication and guide secondary prevention and follow-up after transradial CTO recanalization.

Abstract: Automated fake news detection has advanced substantially through transformer-based classification, yet two critical gaps persist in the literature: static models degrade as misinformation tactics evolve, and high-performing systems rarely reach end users in accessible forms. This paper addresses both gaps through a system that couples RoBERTa-based classification with a post-deployment continuous learning pipeline and a browser-native Chrome extension. We curate a corpus of 70,556 unique articles from three established benchmark datasets—ISOT, WELFake, and the COVID-19 Constraint dataset—after eliminating 42.9% of initially gathered samples as cross-dataset duplicates. A systematic comparison of XGBoost (95.88%), DistilBERT (97.74%), and RoBERTa-base (98.51%) establishes the production model, with selection driven primarily by false negative rate: RoBERTa achieves 1.09%, a 69% reduction over XGBoost and 28% over DistilBERT. A documented vulnerability of transformer classifiers is susceptibility to formally-worded misinformation that mimics journalistic style. We construct a dedicated adversarial training set of 70 examples spanning health misinformation, suppression narratives, and election fraud claims, and demonstrate that targeted fine-tuning raises adversarial detection accuracy from approximately 40% to 95.71% while maintaining 98.60% accuracy on standard benchmarks—achieved through experience replay that prevents catastrophic forgetting. For deployment, ONNX INT8 quantization reduces model size from 500MB to 125MB without accuracy loss, enabling inference on free CPU infrastructure. A GitHub Actions pipeline collects fresh labeled articles nightly, and a FastAPI service running on Hugging Face Spaces serves predictions with 150–200 ms latency. A Chrome extension providing paragraph-level hover detection, LIME-based word attribution, source credibility scoring, and multilingual support across 19 languages makes the system accessible to non-technical users. End-to-end evaluation across 50 curated articles yields 98% accuracy; research-backed adversarial testing across seven categories achieves 91.7%, with perfect detection on adversarial attacks, AI-generated misinformation, temporal domain shifts, and multilingual content.

Abstract: A metal recycling facility scrapyard fire that burned for four days continuously in February 2020 in rural Minnesota resulted in firefighters from around Minnesota to mobilize and aid. Combusted material included cars, refrigerators, metals, glass, foam, insulation. Urine, blood and serum specimens were collected one day later. Parameters collected included: CBC with differential, BMP, blood heavy metals, urine heavy metals, and serum heavy metals. This massive and prolonged industrial fire provided an opportunity for biomonitoring of hazardous, and unique, exposures acutely, in concordance with concerns raised by the employees at risk. Initial analysis of these results did not find evidence of acute concern regarding the biomonitoring results. However, some of these results may portend the potential for long-term consequences such as the development of occupational cancers, especially if there was recurrent exposure in prior or proceeding fires.

Abstract: Background/Objectives: Coexistence of systemic sclerosis and sarcoidosis is very ra-re. Both are systemic autoimmune diseases with lung involvement but with different pathogenesis. In contrast to findings of mid- to upper-lobe interstitial lung disease (ILD) or/with hilar lymphadenopathy in sarcoidosis, the most common lung manifes-tation of systemic sclerosis is lower-lobe ILD, which is typically characterized by a nonspecific interstitial pneumonia pattern. Distinction between lung involvement re-lated to each disease is crucial due to different therapeutic approach Methods We present herein a serie of three overlap cases: two with sarcoidosis onset before the diagnosis of systemic sclerosis and the other with systemic sclerosis onset before sarcoidos. Results: A review of cases of concomitant sarcoidosis and systemic sclerosis is dis-cussed, including the pathophysiology of each disease with shared pathways leading to the development of both conditions in one patient Conclusions: The systemic sclerosis-sarcoidosis overlap is a high-risk phenotype. Early recognition and a personalized, aggressive therapeutic approach are essential to alter the natural history of these two converging fibrotic and granulomatous processes.

Abstract: Background: Hallucination the generation of factually incorrect, internally in consistent, or ungrounded content remains a critical barrier to safe LLM deployment in high-stakes domains. Existing detection methods typically require external knowledge bases, model ne-tuning, or cloud API access, limiting applicability in local inference contexts. Methods: We evaluate the Kerimov–Alekberli (K–A) information-geometric framework as a real-time, inference-time hallucination detector across six open-source LLMs deployed locally on Apple M5 Silicon via Ollama v0.23.2 (Q4_K_M quantisation). The K–A framework monitors the KL divergence between consecutive output distributions relative to a Fisher Information Metric (FIM)-derived threshold (τ = 0.065), triggering First-Passage Time (FPT) alarms when generation departs from the stable Riemannian output manifold. We evaluate 120 responses (6 models × 20 questions) drawn from three established benchmarks: HaluEval (14 questions; categories: Fact, Confuse, Date, Num, Trap), FEVER (4 questions; adversarial fact verification), and SimpleQA (2 questions; precise factual recall). All questions are classified as difficulty level Hard, targeting known LLM failure modes including o-by-one numerical errors, geographical traps, and disputed-attribution confounds. Results: The K–A framework achieves a session hallucination detection rate of 90.9% (20/22 hallucinated responses correctly flagged) with zero false positives on correct responses (0/98). Model-level hallucination rates vary dramatically: deepseekr1:latest (Qwen3 CoT architecture, 5.2GB) exhibits a 95% hallucination rate (19/20 questions) with 100% K–A detection; gemma3:27b (Gemma3, 17.4GB) and gemma3:latest (4.3B, 3.3GB) achieve 0% hallucination. Two K–A false negatives involve con dent factual errors below the KL threshold. Average KL divergence for hallucinated responses (D̅_KL = 0.068 ± 0.004) is significantly higher than for correct responses (D̅_KL = 0.042 ± 0.016). Conclusions: K–A achieves competitive hallucination detection without external knowledge bases, ne-tuning, or cloud infrastructure, processing each response in real time with negligible overhead. The deepseek-r1 result reveals a fundamental tension between chain-of thought reasoning depth and factual precision on concise queries that warrants systematic investigation.

Abstract: (1) Background: Indonesia faces the dual challenge of a high tuberculosis (TB) burden and increasing drug resistance. Conventional molecular diagnostics frequently fail to detect isoniazid resistance and nontuberculous mycobacteria (NTM). This study evaluates a domestic multiplex Open PCR system in Medan, Indonesia. (2) Methods: From July to November 2025, 1,569 sputum specimens from suspected TB pa-tients were analysed using the Indigen MTB/NTM/DR-TB Real-time PCR Kit Gen 2. (3) Results: Mycobacterial DNA was detected in 421 specimens (26.8%). Among these, 396 (94.1%) were drug-susceptible TB, while 16 (3.8%) showed resistance, predominantly INH mono-resistance (n=14; 0.89% of total). Additionally, 9 cases (2.1%) involved NTM or TB-NTM co-infections. Tertiary hospitals showed significantly higher positivity rates (33.5%) than primary care (18.9%; p < 0.001). TB status was significantly associated with male (p = 0.0052) and older age (p = 0.006), whereas resistance profiles and NTM distribu-tion were consistent across all demographic groups (p > 0.80). (4) Conclusions: The Open PCR system effectively identified INH resistance and NTM cases overlooked by standard rifampicin-only assays. By bridging diagnostic gaps across a decentralized referral network, this facilitates rapid and targeted therapy. Integrating multiplex domestic innovations into national diagnostic algorithms is essential for achieving Indonesia’s TB elimination targets.

Abstract: Promising results in the regeneration of skin lesions have been demonstrated with the use of natural (organic) products, such as dermal dressings made of polysaccharides (chitosan complexed with xanthan), as they promote a hydrated and thermally insu-lating microenvironment, allowing gas exchange; and sources rich in growth factors such as autologous platelet-rich plasma (PRPa), which contains transforming growth factor beta (TGF-β), vascular endothelial (VEGF) and platelet-derived (PDGF), re-sponsible for stimulating the inflammatory cascade and healing. The aim of this study was to evaluate the action of a polymeric membrane (chitosan, xanthan and β-glycan) and PRPa on healing in vivo, used alone or in combination. For the tests, rabbits un-derwent a surgical procedure to induce the lesion and were distributed into a control group (GC), membrane group (GM), PRPa group (GPa) and membrane group associated with PRPa (GMPa), evaluated at moments M0, M7, M14, M21 and M28 (28 days). Wound color and exudation, presence of infection and inflammation, formation of granulation, scarring and necrotic tissue, morphological and morphometric analysis were evaluated. Statistical analyzes of the results were performed using the Software R® software, adopting a significance level of 5%. While statistical differences between treatments in healing time were not significant (p>0.05), all wounds achieved 100% retraction by M21. Notably, at M7, PRPa alone and in combination with the membrane contributed to higher wound retraction percentages (29.71% and 21.65%, respectively) compared to the control group (16.96%). These findings suggest that the complexed membrane, alone or combined with PRPa, fosters a humid environment, gas exchange, and antimicrobial activity crucial for healing, with PRPa further enhancing early wound retraction. It is concluded that the treatment of experimental surgical wounds with biodressings such as PRPa alone or associated with a complexed membrane of chitosan, xanthan, and β-glycan significantly contributes to wound retraction, in addition to offering a propitious and indispensable environment for the healing cascade, such as a humid environment, gas exchange, and antibacterial action. Future studies should consider a larger number of animals per group, histological evaluation for global tissue assess-ment, and collagen quantification.

Abstract: In this paper, which is entirely unconditional, we prove a sharpened almost-all theorem with fully explicit effective constants for the restricted weighted Goldbach sum$$R_{a,q}(N)\mspace{6mu}: = \mspace{6mu}\sum_{\substack{p_{1} + p_{2} = N \\ p_{1} \equiv a\ (mod\ q)}}^{}(\log p_{1})(logp_{2}),\quad q \geq 1,\quad gcd(a,q) = 1,$$whose expected main term is $M_{a,q}(N) = C_{2}S(N)N/\varphi(q)$, where $C_{2} = 0.6601618\ldots$ is the twin-prime constant and $S(N)$ is the binary singular series.Our results are organised around four pillars. (I) We give a complete character-pair decomposition of the second moment of the error $E(N): = R_{a,q}(N) - M_{a,q}(N)$, extracting the exact diagonal constant $G/(2\varphi(q))$, where $G = \prod_{p > 2}^{}(1 + (p - 1)^{- 2}) \in \lbrack 1.41320886,1.41320899\rbrack$ is the Gallagher--Goldston constant. (II) We establish a uniform minor-arc $L^{4}$ bound$$\int_{\mathfrak{m}}^{}|S(\alpha)|^{4}\, d\alpha\mspace{6mu} \leq \mspace{6mu}\kappa_{safe} \cdot 2^{A} \cdot \frac{X^{3}}{(logX)^{A}},\quad\quad\kappa_{safe} = 4.40,$$by combining the complete Vaughan identity with the Bombieri--Vinogradov theorem in integral form, giving an explicit derivation of $\kappa_{explicit} = C_{V}^{2}c_{L^{2}} = 4.004$ before applying a rigorous $10\%$ safety margin. (III) We derive the effective almost-all theorem$$\#\left\{ N \leq X\text{ even}:|R_{a,q}(N) - M_{a,q}(N)| > C(A,q)\, N(logN)^{- 3} \right\}\mspace{6mu} \ll_{A,q}\mspace{6mu} X(logX)^{- A},$$with the explicit constant $K: = 2C(1,4) \leq 38.02$, obtained from $C(1,4) \leq 19.01$ via a Stechkin-type optimisation. (IV) We prove a Pintz-type exceptional-set bound on $\{ N \leq X:R_{a,q}(N) = 0\}$.Every statement in the main body carries the tag \[PROVED\]. No Generalised Riemann Hypothesis, no zero-density hypothesis, no ternary sum $W_{a,q}(n)$, no spectral input, and no Chen-type sieve are used anyware.

Abstract: Inhomogeneous magnetic field distributions in high-frequency planar transformers frequently cause severe localized thermal hotspots and elevated leakage inductance. Traditional interleaved winding designs rely heavily on empirical trial-and-error, which becomes computationally prohibitive for multi-layer parallel structures due to the factorial "curse of dimensionality." To address this bottleneck, this paper proposes a universal, data-driven optimization methodology. First, a quantitative one-dimensional prefix-sum model is established to correlate winding arrangements with spatial magnetomotive force (MMF) distributions, effectively simplifying the electromagnetic evaluation. Subsequently, a customized Genetic Algorithm (GA) framework, featuring physical-constraint-preserving operators such as Order Crossover (OX), is introduced to efficiently navigate the high-dimensional discrete search space. Using an extreme 26-layer complex parallel winding configuration (Np:Ns = 9:2) as a primary case study, the proposed GA method effectively bypasses over 1.5 million permutations, converging to the global optimum within 100 generations. The optimized structure achieves profound peak-shaving, drastically reducing both the peak MMF and total uncoupled magnetic energy area. This methodology provides a systematic, computationally lightweight EDA solution that fundamentally replaces empirical trial-and-error in the design of high-frequency magnetic components.

Abstract: Nonlinear dynamical systems often exhibit complex collective behavior arising from the interaction of multiple elementary modes. In this work we investigate the aggregation of a countable family of dynamical modes generated by Lotka-Volterra systems and study the resulting structure in a Hilbert space of observables. The classical Lotka-Volterra equations form a fundamental class of nonlinear models describing interacting populations through coupled differential equations, while Koopman operator theory provides a framework in which nonlinear dynamics can be represented as a linear evolution acting on observable functions.We show that a countable aggregation of such dynamical modes admits a well-defined limit in a Hilbert space when the coefficients belong to l2. The resulting aggregated observable evolves according to the associated Koopman semigroup, yielding a linear representation of the underlying nonlinear dynamics in the observable space. We further prove that the geometry induced by this aggregated dynamics admits a canonical class of equivalent metrics generated by coercive operators, ensuring that the stability topology of the system is independent of the particular metric chosen within this class.Finally, we illustrate the theoretical framework by introducing a social risk functional defined as a quadratic observable associated with the induced metric. This example demonstrates how application-specific quantities can naturally arise from the geometric structure generated by aggregated nonlinear dynamics.