Abstract: Zonadhesin (ZAN) is a sperm protein currently known for its role in binding to the oocyte zona pellucida. Although its localization has been described in ejaculated and capacitated spermatozoa from mice, pigs and rabbits, its distribution following the acrosome reaction remains poorly understood. Here, we characterized ZAN localization in rabbit, boar, and bull spermatozoa under in vitro conditions mimicking early fertilization events. Ejaculated spermatozoa, swim-up-selected spermatozoa in capacitation medium, and acrosome reaction-induced spermatozoa were analyzed. Immunofluorescence was performed using an antibody against the MAM domain of ZAN to determine its localization and PNA-FITC to assess acrosomal status, while protein abundance was assessed by quantitative LC-MS/MS. Consistent with previous reports, ZAN was detected in the anterior region of intact spermatozoa. However, the MAM-specific antibody also revealed post-acrosomal localization. Species-specific patterns were observed in intact spermatozoa: rabbit and bull showed acrosomal staining with or without post-acrosomal labeling, whereas boar displayed predominant pre-equatorial and post-acrosomal localization. Although ZAN labeling decreased after acrosomal exocytosis, the protein was consistently retained in the post-acrosomal region. These findings suggest ZAN contributes not only to sperm–ZP binding but also to later fertilization events, including sperm–oolemma interaction and membrane fusion.

Abstract: This paper reviews requirements for water supply rate for life support of human crews on deep space missions such as Mars, and methods to provide that water supply. The literature on required water supply flow rate to support human crews on deep space missions is inadequate, typically with a few terse estimates lacking analysis or explication. These estimates were generated in an era where saving mass was critical and the allocations were skimpy. Here, we provide new, updated estimates of suggested water supply flow rate (at three levels of comfort) to support human crews on deep space missions in an era where mass in deep space is far more affordable. The total mass of water required for the mission is significant, but appropriate in the era of huge launch vehicles like the Starship. It was widely believed that water recycling systems are necessary to reduce mission mass in the era of high launch costs. However, the reliability of recycling technology is poor, as evidenced by experience on the International Space Station. Use of spares to replace subsystems that fail was proposed to greatly improve reliability, and that works good on paper as shown by probabilistic analysis, but the logistics of implementation are problematic. Bringing water from Earth is the best way to supply crew requirements for limited missions likely to be the first human landings on Mars. For futuristic missions of great extent, either recycling or use of indigenous water from Mars would be needed. In any mission, if possible, bringing a survival level of water from Earth is strongly recommended.

Abstract: Background: Radiography is a health profession that employs ionizing and non-ionizing radiations for diagnostic and therapeutic purposes. Students from other health professional courses share institutional and clinical environments with radiography students throughout their training, making mutual understanding of the profession professionally important. No study had previously assessed this relationship at Bayero University Kano. Objectives: To assess the knowledge and perception of students from other health professional courses in Bayero University Kano with respect to radiography profession. Methods: A prospective, cross-sectional study was conducted among other health professional departments. Stratified random sampling with proportionate allocation was used to select 322 respondents. Data were analyzed using SPSS version 22, applying descriptive statistics, Pearson correlation, and independent samples t-tests. Results: Of 322 questionnaires distributed, 306 (95.0%) were returned and fully completed (response rate of 95%). Medical Laboratory Sciences students recorded the highest knowledge score (87.5%) while Physiotherapy students recorded the lowest (48.1%). Optometry students held the most favorable perception of the profession (96.2%) while Physiotherapy students were the least favorable (66.7%). Strong positive correlations between knowledge and perception were found in MBBS (r = 0.737, p < 0.001), Physiotherapy (r = 0.681, p < 0.001), and Dentistry students (r = 0.658, p < 0.001). Conclusions: With the exception of Physiotherapy students, participants from other health professional courses at Bayero University Kano demonstrated satisfactory knowledge and generally favorable perception of radiography. Interprofessional educational initiatives are recommended to address the gaps identified.

Abstract: We establish the unique topological setting of any unified gauge theory with quantized charge, and derive its physical consequences. A gauge field is a principal bundle equipped with a gauge symmetry and connection potential. We prove that (1) given electromagnetism as a U(1) gauge theory with quantized charge, and (2) the existence of a unified single-field theory, a unified theory must be formulated, up to homotopy equivalence of the base and isomorphism of bundles, on the universal complex Hopf fibration bundle S¹ → S^∞ → CP^∞ and its finite approximations S¹ → S²ⁿ⁺¹ → CPⁿ. Completeness and indecomposability are derived consequences, not additional axioms. The Standard Model gauge groups arise as natural reductions along the nested shell hierarchy: U(1) from the circular S¹ fiber, SU(2) from the S³ shell and SU(3) from the S⁵ shell. The classifying spaces BU(1), BSU(2), and BSU(3) are all internal to this single hierarchy; each is obtained by changing the quotient on the same universal total space S^∞, not by independent construction. The unified structure group G_total = (SU(3) × SU(2) × U(1) × SO(4))/Γ is intrinsically non-factorable due to the generating role of the universal first Chern class in H^∗(CP^∞;Z) ≅ Z[c₁]. The unique universal action on the Hopf bundle is derived from SO(4)-equivariance, the Killing form, and degree classification; the torsion action is the unique admissible positive-definite quadratic form. The Einstein, Maxwell, and Yang–Mills field equations all follow from this single action. The Beltrami operator B = ⋆d|ξ on the contact distribution is doubly forced as both the action Hessian and the unique equivariant first-order operator. The result is a topologically enhanced Standard Model: every term of the conventional SM Lagrangian appears with identical structure, with no free parameters, and with gravity via Chern–Simons theory on S³, the Beltrami mass operator, and the resolution of the strong CP problem as enhancements. Gravity emerges on the S³ = SU(2) shell, sharing exactly one generator—the Cartan U(1)—with the gauge sector; gauge–gravity unification is the fibration U(1) → SU(2) itself. On each Hopf shell, the Beltrami operator is elliptic, essentially self-adjoint, and possesses a discrete spectrum stable under torsion perturbations by the Kato–Rellich theorem. Fiber winding decomposition yields independent topological sectors whose Gaussian functional determinants, regularized via spectral zeta functions, generate intrinsic mass scales. Fermion mixing (CKM, PMNS) arises from intersection-form overlaps of admissible cycles in H^∗(CP⁴), with CP violation induced by fiber holonomy phases. The electroweak vacuum expectation value v serves as the unit conversion factor between geometric and laboratory scales; given this single identification, the fine-structure constant and all shell-specific mass scales, spectral coefficients, and interaction strengths entering the particle spectrum are fixed by the spectral geometry of the complex Hopf fibration. The framework predicts the complete particle mass spectrum and anomalous magnetic moments, with suggested independent experimental tests (torsion-induced phase wobble, absolute neutrino mass scale, and the electron, µ and τ g − 2) providing falsifiability. Fundamental constants arise from topological normalization. Further results include anomaly cancellation, dark sector effects from bundle torsion and holonomy, and the elimination of singularities. The mathematical results stand independently as contributions to the topology of classifying spaces, reductions along nested Hopf shells, and contact spectral geometry.

Abstract: Molecular residual disease (MRD) testing approaches with plasma next-generation sequencing (NGS) testing to identify circulating tumor DNA (ctDNA) in resectable stage non-small cell lung cancer (NSCLC) are evolving. The MRD concept is to better guide perioperative systemic treatment and identify recurrent NSCLC before symptomatic radiographic recurrences. Multiple tumor-informed assays are available with technology driving lower levels of ctDNA detection. However, it remains unclear that individual patients derive survival outcome benefit from MRD testing. NSCLC tumor biology of spatial heterogeneity, early parallel metastases, and recurrence clonal evolution can impact tumor-informed approaches irrespective of specific assay level of ctDNA detection. Clinical decision making guided by tumor-informed MRD testing to date have been limited by recurrence risks of up to 25% when landmark MRD negative, improved outcomes benefit of adjuvant treatment even when landmark MRD negative, and lead times with longitudinal MRD positive conversion of several months or longer before overt radiographic recurrences with no proven strategy of survival benefit with intervening treatment. Cautionary tumor biology and clinical issues remain in the clinical utility of tumor-informed MRD testing in resected NSCLC. These need to be clarified with certainty before MRD testing should step beyond a technology driven prognostic recurrence risk indicator before becoming an absolute clinical guide to meaningfully impact individual patient management and outcomes.

Abstract: Many results in quadrilateral geometry are traditionally stated for convex quadrilaterals. In this paper, we show that several of these results remain valid for self-intersecting quadrilaterals. In particular, we prove that, for any vertex, the maltitudes (midpoint altitudes) corresponding to two adjacent sides and the associated diagonal are concurrent; we call this point the malticenter of the vertex. This result holds uniformly for both simple and self-intersecting quadrilaterals. We further relate malticenters to classical centers (centroid, circumcenter, and orthocenter) via homotheties. Finally, we prove a conjecture of [1], previously observed for convex quadrilaterals, showing that \[ \operatorname{Area}(ABCD)=\operatorname{Area}(H_AH_BH_CH_D) \] holds for all quadrilaterals, where $H_A,H_B,H_C,H_D$ are the orthocenters of the triangles formed by the vertices of $ABCD$.

Abstract: Primary tracheal neoplasia is uncommon in domestic animals and humans, and most reported tracheal tumors are malignant. To the authors’ knowledge, this case represents the third confirmed tracheal leiomyoma reported in dogs. Similarly, in human medicine, tracheal leiomyomas have only been reported sporadically and account for approximately 1% of tracheal tumors. A 12-year-old spayed female Pitbull was presented as an emergency because of worsening recurrent respiratory signs that were refractory to medical treatment. On initial evaluation, reduced mobility of both arytenoid cartilages was observed, and left arytenoid lateralization was therefore performed. However, the patient continued to experience severe episodes of respiratory distress requiring orotracheal intubation. Subsequent bronchoscopy revealed an intraluminal tracheal mass partially obstructing the airway lumen. Because of this obstruction, an emergency temporary tracheostomy was performed caudal to the mass. Once the patient was clinically stabilized, computed tomography was performed to complete surgical planning. Surgical treatment consisted of segmental tracheal resection and end-to-end anastomosis, with removal of 24% of the total tracheal length. Histopathological examination confirmed the diagnosis of tracheal leiomyoma. Complete surgical excision was achieved, supporting a favorable prognosis.

Abstract: Autonomous driving technology imposes stringent requirements on real-time environmental perception and dynamic distance measurement, which are critical prerequisites for vehicle path planning and driving safety. Traditional ranging methods relying on LiDAR and visual sensors often suffer from poor real-time performance and insufficient robustness in complex and dynamic traffic scenarios. To address this limitation, this paper proposes a novel fixed-time zeroing neural network (ZNN) to achieve high-precision and real-time inter-vehicle distance estimation for autonomous vehicles. First, a time-varying optimization model for inter-vehicle distance calculation is established based on dynamic programming theory, which fully considers the motion trajectories and structural constraints of adjacent vehicles. Subsequently, a dedicated activation function is designed to construct the improved fixed-time ZNN model for solving the above time-varying optimization problem. Rigorous theoretical proofs are presented to verify the fixed-time stability of the proposed network, and a tight upper bound of the convergence time is analytically derived. Moreover, comprehensive parameter selection strategies are discussed to guide practical model deployment. Finally, numerical simulation results demonstrate that the developed ZNN model possesses faster convergence speed and stronger robustness compared with existing methods, and it can accurately complete real-time distance calculation within a fixed time upper bound. The proposed method provides a new effective solution for dynamic ranging tasks in autonomous driving systems.

Abstract: The rapid growth of battery-driven electric three-wheelers in Bangladesh has significantly increased the demand for electricity used for battery charging, placing additional pressure on the national power grid. Although these vehicles offer affordable and environmentally friendly transportation, their heavy dependence on grid electricity has become a growing concern for the country’s energy sector. This study presents the design and evaluation of a solar-supported electric three-wheeler that uses a rooftop photovoltaic (PV) solar panel to assist battery charging and reduce reliance on conventional electricity. The proposed system includes a 48 V battery pack, an 800 W differential motor, a 400 W rooftop solar panel, and an MPPT charge controller. The research evaluates the system’s energy generation, charging performance, operating range, and overall feasibility under practical operating conditions in Bangladesh. The results show that the rooftop solar panel can supply additional energy during daytime operation, helping to extend vehicle runtime and reduce battery discharge from grid charging. This study found that the proposed solar-assisted system can contribute to sustainable transportation, encourage the use of renewable energy, and help to reduce pressure on Bangladesh’s electricity system along with global ecosystem.

Abstract: RNA-binding proteins (RBPs) are essential regulators of RNA metabolism and gene expression, influencing processes such as splicing, stability, localization, and translation. Despite their critical roles in health and disease, including cancer, identifying RNA-protein interactions remains challenging due to technical limitations and biases of existing methods. Here we review and compare experimental techniques—including in vitro affinity purification, in vivo cross-linking, and proximity labeling—and computational prediction tools for RBP identification. We assess their strengths, limitations, and applicability across biological contexts, emphasizing the benefits of integrating experimental and computational strategies. Our analysis provides practical guidelines for selecting appropriate methodologies tailored to different cell types and research goals. These insights aim to facilitate more accurate mapping of RNA-protein interactomes, thereby advancing understanding of RBP functions and supporting the development of novel therapeutic interventions targeting RNA-protein complexes.

Abstract: Identifying Coffea arabica genotypes that combine high cup quality and consistent sensory performance across harvests is essential to breeding programs targeting specialty coffee production. This study aimed to characterize the sensory quality of Coffea arabica genotypes and to assess their consistency across two consecutive harvests. Thirty-seven C. arabica accessions maintained in the EPAMIG Active Germplasm Bank, located in Patrocínio, Minas Gerais, Brazil, were evaluated during the 2020 and 2021 harvest seasons. Fruits were harvested at the cherry stage, dry-processed to obtain natural coffee, and sensorially evaluated according to the Specialty Coffee Association (SCA) protocol. Cup intensity attributes, final score, prevalence of aroma and flavor nuances, across-harvest agreement, principal component analysis, and Spearman correlation were assessed. Phenotypic data were further analyzed using a linear mixed model to estimate variance components, the genotype × harvest interaction, and repeatability. All genotypes scored above 80 points and were therefore classified as specialty coffees, ranging from 81.21 to 85.59 points. The genotype × harvest interaction was significant and exceeded the genotypic variance; consequently, the genotype effect was not significant when tested against the interaction mean square, resulting in low across-harvest repeatability (H2 = 0.30). Agreement analysis indicated a mean reduction of 1.64 point in 2021 relative to 2020, with wide limits of agreement (−4.70 to 1.44 points) and a low, non-significant intraclass correlation coefficient (ICC = 0.077), evidencing the harvest effect on sensory quality. Despite the overall low agreement between harvests, accessions MG 1196, MG 1175, and MG 1197 combined high final scores with the smallest variation between the two harvests. Multivariate analysis indicated that cup quality was more closely associated with body, sweetness, and aftertaste. The fruity, floral, and sweet nuances showed positive correlations with the final score. Taken together, these findings suggest that selecting promising coffee accessions should simultaneously consider overall cup quality, harvest-to-harvest consistency, and the frequency of key sensory descriptors.

Abstract: With the rapid advancement of LLM capabilities, expectations for AI agents are shifting from solving simple, single-turn tasks toward carrying out long-horizon tasks in the real world. We refer to such systems as long-horizon agents: agents that plan over extended horizons, interact with real-world environments, recover from their own mistakes, and adapt their strategies during execution. This capability is rapidly becoming the central bottleneck for practical agent intelligence. Despite this progress, the field still lacks a shared definition and taxonomy for long-horizon agents. Related concepts such as "self-evolving" or "autonomous" agents are often used interchangeably, none of which clearly captures what it means to build a long-horizon agent. This gap leaves the community without a principled way to attribute advances in long-horizon competence. This paper offers a unified landscape by framing long-horizon agency as the co-evolution of an externalized harness and an internalized optimization, and organizes the paper around six connected perspectives: Foundation, Evolution, Harness, Optimization, Application, and Frontier. We first formalize long-horizon agency as a harness-coupled decision process and distinguish it from neighboring concepts such as long-running execution, autonomy, and self-evolution. We then trace the field's evolution from prompt-level control to runtime agent systems, classifying existing work through the complementary lenses of externalized harnesses and internalized optimization. Building on this view, we organize five application forms of long-horizon agents by their interfaces, and review the corresponding benchmarks and resources. Finally, we discuss key challenges and frontier directions. Looking ahead, we hope this paper serves not only as a reference for existing work, but also as a foundation for building the next generation of capable, reliable long-horizon agents.

Abstract: Fungal infections are an increasingly important yet underrecognized global health threat. Climate change, environmental disruption, and intensified human–animal interactions are shifting fungal ecology, enabling pathogens to push beyond traditional geographic and thermal boundaries. Increasing temperature, shifting humidity, and extreme weather events have favoured the emergence and reemergence of fungal disease, as reflected in the rapid global dissemination of Candida auris, in a manner defying conventional models of pathogen spread. The environmental drive to fungal adaptation includes increased thermotolerance and survival under hostile conditions for the infection of endothermic hosts. At the human-animal-environment interface, the zoonotic spillover accelerates fungal evolution toward increased virulence and antifungal resistance. Resistance to all major classes of antifungal drugs is increasingly observed and “seriously challenges treatment, leading to persistent infections and a greater healthcare burden.” Despite advances in molecular diagnostics and genomic surveillance, significant gaps in our understanding of fungal transmission, host adaptation, and resistance mechanisms remain. This review focuses on climate-driven fungal emergence, its zoonotic potential, antifungal resistance, and current detection strategies that call for immediate action through integrated One Health surveillance and coordinated global responses.

Abstract: Construction and demolition waste (C&amp;DW) has been investigated both for radionuclide sorption and as a precursor for geopolymer materials. However, research on C&amp;DW-derived geopolymers has primarily focused on synthesis and characterization, while their role in radionuclide immobilization remains insufficiently explored. This review evaluates C&amp;DW-derived geopolymers as promising matrices for radionuclide immobilization, focusing on retention capabilities and factors influencing immobilization performance. Available studies indicate that waste-derived geopolymer systems can limit radionuclide mobility and leaching, but their performance strongly depends on precursor composition, phase assemblage, and matrix structure. The mineral complexity of C&amp;DW-derived matrices may provide diverse retention pathways, supporting their consideration as immobilization materials. Linking the documented sorption capacity of C&amp;DW materials with the immobilization potential and favorable characteristics of C&amp;DW-derived geopolymer matrices represents a promising approach for developing advanced systems for radionuclide solidification. Due to the limited number of studies directly addressing radionuclide immobilization in C&amp;DW-derived geopolymer systems, evidence from related studies is considered to support assessment of their immobilization capacity. Nevertheless, further clarification is required regarding the integration of existing research findings, precursor heterogeneity, multi-ion interactions, and long-term performance under realistic conditions. Addressing these limitations through systematic investigations is essential to support their application in radioactive waste (RW) management.

Abstract: This review reports on the huge potential of natural products (NPs) as drugs due to their pleiotropic activities and discusses the recent research and development of nanoscale drug delivery systems loaded with NPs. Indeed, the number of publications is dramatically increased in the last years and excellent biopharmaceutical properties of nanosized vectors loaded with NPs have been reported, however on the market the number of products based on nanoscale drug delivery systems are limited essentially to food supplements and cosmetics. The difficulties of NPs loaded nanovectors to reach the market as medicine is mainly due to the lack of dedicated regulatory frameworks, a specialized "nano" legal context. Instead, nanovectors are evaluated on a case-by-case basis under existing broad pharmaceutical regulations under traditional benefit/risk frameworks. This manuscript would be a comprehensive collection of the reviews on nanovectors loaded with some paradigmatic NPs, namely curcumin, quercetin, resveratrol, epigallocatechin-3-gallate, thymoquinone, cannabidiol, and silybin, all developed to overcome their biopharmaceutical restrictions, mainly solubility and stability. The study highlights the challenges and limitations of the reported studies, evidencing in many cases the lack of complete knowledge of the mechanistic of nano–bio interactions, the lack of some basic requirements as the encapsulation efficiency and drug loading efficiency, as well as the very limited number of the clinical studies. Finally, NPs are presented as multifunctional excipients of nanovectors to improve nanocarrier structure, function and drug biopharmaceutical properties, mainly represented by ginseng and quillaja saponins, escin and glycyrrhizin to form micelles or vesicles such as escinosomes.

Abstract: Background. The American Heart Association (AHA) introduced “Life’s Essential 8” as a comprehensive framework to promote cardiovascular health (CVH) and prevent cardiovascular diseases (CVDs). Despite this, the prevalence of optimal CVH remains low in most developed populations. Molecular hydrogen (H₂) has shown therapeutic potential in CVD, obesity, type 2 diabetes mellitus (T2DM), and neuropsychological disorders, suggesting a possible integrative role in CVH promotion and disease prevention. Review of Data. The AHA’s 8 components include healthy diet, physical activity, nicotine avoidance, adequate sleep, optimal body weight, and regulation of blood lipids and glucose, as well as blood pressure. Accumulating evidence indicates that H₂ may beneficially modulate most of these domains. In a randomized controlled trial involving 60 patients with metabolic syndrome, hydrogen-rich water (HRW) significantly reduced body mass index (BMI), blood lipids, glucose, and HbA1c, and improved inflammatory and redox biomarkers compared to placebo. Additional studies suggest that H₂ can lower blood pressure and its variability, enhance physical performance, and favorably modulate gut microbiota, including increased production of short-chain fatty acids. Hydrogen therapy, administered as H₂-rich water or H₂–O2 inhalation, has also been associated with improved sleep quality, potentially through attenuation of oxidative stress and psychological distress. Overall, up to seven of the eight AHA CVH metrics may be influenced by H2 intervention. H₂ may function as a bioactive therapeutic agent and dietary adjunct that improves multiple determinants of CVH. Its integration into preventive and therapeutic strategies may facilitate attainment of AHA-defined CVH, particularly in populations at elevated risk of CVDs as well as pre-metabolic syndrome.

Abstract: Cold-pool structure controls the confinement and transport environment relevant to surface wintertime ozone in the mountainous Uinta Basin, Utah, USA, but point surface values alone do not establish that structure. We evaluated deterministic responses in Weather Research and Forecasting (WRF) simulations of the 2 February 2013 episode to the supplied Global Forecast System (GFS) or North American Model (NAM) driving analysis, nest feedback, boundary-layer and surface-layer treatment, slope-aware radiation, and static-terrain source. Across a common five-hour sample, GFS-driven members were warmer at the evaluated surface sites, approximately 3.6 K less stable through 50–500 m above ground level, and 0.8–1.0 m s−1 faster in fixed-layer transport wind than feedback-matched NAM members. GFS-driven members also retained a smaller footprint-mean, vertically integrated heat deficit under all seven definitions, although every simulation gained heat deficit over the retained window. The repeated separation is therefore a driving-product state response rather than demonstrated faster cold-pool loss. Controlled feedback and physics responses were smaller and metric dependent, while bounded terrain and fine-grid process diagnostics showed spatial structure that the station sample could miss without establishing terrain superiority, resolution benefit, basin export, or inversion depth. The study provides a meteorological result with implications for subsequent air-chemistry modelling; it does not contain a chemistry calculation or identify the initial-versus-lateral-boundary contribution to the driving-product response.

Abstract: Disinfection of livestock facilities under modern intensive production systems remains an effective strategy for controlling microbial contamination. Breaking the chain of the infectious process at the initial stage with the help of effective chemical agents is the key to maintaining animal health and preserving their productivity. Housing dairy cows in free-stall group pens improves animal welfare but also increases opportunities for contact between animals, thereby increasing the risk of microbial transmission. Our in vitro study successfully determined the effective cidal concentrations of three different multicomponent disinfectants against a range of opportunistic microorganisms. For this purpose, the individual sensitivity of each type of microorganism commonly found in dairy farms to different concentrations of disinfectants was determined. The iodine-based disinfectant achieved complete cidal activity at a concentration of 5%, while the aldehyde+QAC-based disinfectants showed cidal activity at a 1% concentration of the working solution. The results highlight the importance of using appropriate concentrations and taking into account the specific microbial profile of dairy livestock facilities to achieve effective disinfection and prevent the development of resistance. The data provide valuable information for establishing disinfectant rotation strategies in dairy farm hygiene protocols.

Abstract: We introduce ZPIF (Zero Pair Interaction Functional) as a revolutionary Quadratic Spectral Variant (QSV) that fundamentally redefines the Scale Regulated Aggregation (SRA) framework and Riemann's classical explicit formula. At the heart of this work lies the concept of pair interactions: the regulated second-order self-interactions between spectral modes, which capture the nonlinear coupling of each zero with itself and with neighboring zeros. Departing from the traditional linear spectral decomposition, ZPIF introduces a novel quadratic term $\lambda \sum \gamma_n^2 |c_n|^2$ that explicitly encodes these pair interactions within a rigorous Hilbert space formulation. This term represents the first mathematical framework to systematically incorporate pair-wise spectral couplings into the explicit formula, revealing emergent nonlinear behaviors that are entirely absent from classical models. The framework delivers: • A rigorous operator definition with spectral expansion and trace-class regularization. • Conditional convergence under truncation, ensuring mathematical consistency. • Numerical simulations using the first 100 non-trivial zeta zeros, which reveal distinct nonlinear growth and quadratic interaction effects directly attributable to pair interactions. The quadratic interaction term $\lambda \sum \gamma_n^2 |c_n|^2$ introduces a novel spectral energy functional that aligns structurally with the SRA law, positioning ZPIF as a foundational tool for exploring quadratic spectral phenomena. This study does not claim to resolve the Riemann Hypothesis but offers a transformative mathematical proposal with potential applications in signal processing, quantum systems, and complex dynamical networks.This work represents the first joint articulation of ZPIF as an SRA-aligned revolutionary variant, honoring the interpretive contributions of Elsayed and the foundational framework of Vogt, and inaugurating a new era in collaborative mathematical research.

Abstract: (1) Background: Stroke remains a leading cause of long-term disability, with 80–90% of survivors experiencing gait disturbances. Functional electrical stimulation (FES) is widely used to improve motor recovery and gait; however, its effectiveness remains uncertain because outcomes vary across studies. This systematic review evaluated the effectiveness of FES, alone or combined with rehabilitation strategies, for gait recovery in individuals with chronic stroke. (2) Methods: A systematic search of the Cochrane Library, PubMed, EMBASE, MEDLINE, and Web of Science identified randomized controlled trials published between 2016 and 2026. Adults with chronic stroke receiving lower-limb FES, alone or combined with conventional rehabilitation, were included. Outcomes included gait performance, balance, motor function, and activities of daily living. Methodological quality was assessed using the Cochrane Risk of Bias 2 tool. (3) Results: Eleven studies involving 328 participants were included. FES improved gait speed, balance, lower-limb motor function, and functional independence, particularly when combined with task-specific rehabilitation. Improvements in coordination, neuromuscular activation, propulsion, reactive balance, and corticospinal excitability also supported its role in motor recovery. (4) Conclusions: FES is a relevant adjunctive intervention for post-stroke rehabilitation. Although methodological heterogeneity remains, current evidence supports its potential to improve gait and functional outcomes.