Abstract: This work presents a comprehensive investigation of the thermal decomposition of nickel oxalate dihydrate as a precursor for the synthesis of porous NiO, with particular emphasis on microstructural formation and evolution. The transformations occurring at successive stages of the reaction were examined using SEM, TEM, N₂ adsorption, TG–DSC–MS, and in situ powder XRD, enabling the mechanisms of pore formation to be elucidated. The decomposition results in the formation of a porous pseudomorph composed of NiO nanoparticles with an average size of approximately 4 nm. The resulting microstructure exhibits hierarchical porous architecture. During dehydration, macropores are generated as a result of crystal fragmentation into blocks several hundred nanometers in size. Subsequent oxalate decomposition leads to the formation of mesoporous aggregates composed of nanometer-sized particles. The factors governing the parameters of the porous microstructure are analyzed. Owing to its hierarchical pore system, the obtained NiO demonstrates significant potential for applications in heterogeneous catalysis, gas sensing, electrodes for super-capacitors and Li-ion batteries, and photoelectrochemical devices. In such systems, macropores facilitate mass transport by reducing diffusion resistance, while mesopores provide a high accessible surface area for adsorption and catalytic reactions.

Abstract: Instructor clarity is a central component of instructional communication and has been consistently associated with positive academic outcomes; however, less evidence exists regarding the mechanisms through which it influences student interest in higher education contexts. The present study examined a structural model in which instructor clarity predicts student interest both directly and indirectly through students’ academic satisfaction and state motivation. A total of 258 undergraduate students from the University of Extremadura enrolled in the Bachelor’s Degree in Early Childhood Education and the Bachelor’s Degree in Primary Education participated in the study. Data were analyzed using Partial Least Squares Structural Equation Modeling (PLS-SEM), including an assessment of the model’s predictive capability. The results indicated that instructor clarity was positively associated with academic satisfaction, state motivation, and student interest, with the first two variables acting as complementary mediators in these relationships. The model demonstrated high predictive power and strong predictive validity with respect to student interest. Overall, the findings suggest that instructor clarity constitutes a relevant mechanism in shaping student interest by structuring the academic experience and fostering positive motivational states, highlighting the importance of promoting clear teaching practices in university faculty training and evaluation processes to enhance students’ learning outcomes.

Abstract:

The retromer is a highly conserved complex that mediates the trafficking of cargo proteins to plasma membrane or trans-Golgi network. In pathogenic microorganisms, retromer-dependent transport contributes to the delivery of virulence factors and promotes infection. The retromer consists of a sorting nexin dimer (SNX) and a cargo-selection complex (CSC), formed by Vps26, Vps35, and Vps29. In Entamoeba histolytica, the parasite causative of human amoebiasis, the retromer functions as a Rab7A GTPase effector and participates in phagocytosis and cytotoxicity. Although we previously characterized the roles of EhVps26 and EhVps35, the function of EhVps29 remained unclear. In this study, we analyzed the subcellular localization and functional role of EhVps29 in adhesion, phagocytosis, and cytopathic effect. EhVps29 localized to the plasma membrane, cytosol, vesicles, tubules, Golgi-like structures, MVBs and, for the first time, in the nucleus. Immunofluorescence and western blot assays demonstrated that EhVps29 modulates the localization of the EhVps26, EhADH adhesin and EhCP112 cysteine protease. The Ehvps29 gene silencing and overexpression confirmed its involvement in virulence-associated processes. Immunoprecipitation and confocal microscopy results showed the interaction among EhVps29, EhVps36 and EhADH ESCRT machinery members. Our results indicate that EhVps29 is involved in parasite virulence and protein trafficking through recycling or degradation pathways.

Abstract: Automatic speech recognition has advanced rapidly for high-resource languages, yet performance remains limited for low-resource languages such as Bangla, particularly in telehealth settings. Most systems rely on a standardized 16 kHz sampling rate, a design choice despite evidence that Bangla contains sibilant fricatives and other phonetic cues with substantial high-frequency energy that may be suppressed under bandwidth and latency constraints. This study evaluates audio sampling rate as a controllable signal-level parameter for Bangla telehealth ASR to identify an empirically grounded operating range balancing transcription accuracy, execution time, and network bandwidth. Twenty real-world Bangla doctor–patient consultations recorded at 32 kHz were deterministically resampled to 55 configurations between 8 kHz and 32 kHz and transcribed using a fixed cloud-based ASR system. Session-level Word Error Rate, execution latency, payload bandwidth, and high-frequency phonetic content were analyzed using a composite sibilant-likelihood score. WER decreased from 0.338 at 8 kHz to a local minimum of 0.232 at 18.75 kHz, with gains plateauing beyond this range despite substantial bandwidth increases. Elbow-point, Pareto frontier, weighted scoring, and Minimum Acceptable Trade-off analyses converged on an optimal region between 17.25 and 18.75 kHz, demonstrating that sampling-rate optimization improves ASR accuracy without proportional resource costs in telehealth settings.

Abstract: Peptides are short chains of amino acids with a unique pharmacological niche between small-molecule drugs and large proteins. Their use in sports medicine is rapidly expanding, driven by patient demand for accelerated injury recovery and performance enhancement. While numerous peptide drugs have undergone a rigorous approval process that evaluates both safety and efficacy, a parallel "gray market" of unapproved compounds has emerged, operating largely outside regulatory oversight. Our objective is to present the pharmacological mechanisms, safety profiles, and regulatory status of prominent approved and unapproved peptides marketed direct to patients, including AOD-9604 (Anti-Obesity Drug 9604), BPC-157 (Body Protection Compound 157), CJC-1295, FS-344 (Follistatin-344), GHK-Cu (Glycyl-L-histidyl-L-lysine copper), ipamorelin, MOTS-C (Mitochondrial ORF of the 12S rRNA type-c), sermorelin, SS-31 (Elamipretide), tesamorelin (Egrifta), thymosin beta-4, and TB-500 (thymosin beta-4 fragment). Many unapproved peptides demonstrate favorable tissue repair and metabolic outcomes in animal models, but rigorous human safety data is scarce, and there is potential for serious harm. This narrative review focuses on peptide utilization in sports medicine and alternative treatments for specific peptides. We provide a framework to navigate patient discussions about peptides to better facilitate evidence-based practices for musculoskeletal healing and athletic performance. We also discuss the placebo effect as a mediator of peptide efficacy, and how social media amplifies this effect.

Abstract: The Hodgkin-Huxley (HH) model has dominated quantitative neuroscience since 1952. Its authors explicitly acknowledged its phenomenological character and called for a deeper mechanistic account. We propose that this account is the IMH model of nerve conduction. The model rests on three biophysical foundations: (1) the polyelectrolyte gel framework of Ling, in which intracellular K⁺ is adsorbed on protein sites and the resting ionic distribution is a thermodynamically stable Donnan equilibrium requiring no metabolic pump; (2) the Hofmeister ion series, which governs differential adsorption of K⁺ versus Na⁺; and (3) the hydraulic wave equation for a fluid-filled elastic tube, which predicts conduction velocity from myelin elastic modulus rather than sodium channel density. In this framework, the action potential is a coupled ionic-hydraulic phase transition propagating as a pressure wave in the periaxonal space. Electrical events are causally secondary — the electromagnetic shadow of the hydraulic wave, not its cause. We demonstrate that the model resolves a 75-year-old anomaly identified but left unexplained by Huxley and Stämpfli in 1949: positive current enters a node before the membrane potential reaches its maximum, a relation the authors themselves described as "impossible in a system of resistances and capacities." We present nine falsifiable predictions distinguishing the IMH model from HH, covering myelin mechanics, mechanoreceptor adaptation, terminal arborisation geometry as the physical substrate of the Umwelt, motor tremor as hydraulic interference, the temporal basis of conscious perception, and the coupled physical constraints that explain why large-diameter unmyelinated fibres do not exist in nature.

Abstract: We summarize the key aspects of the ongoing octonionic E₈ ×ωE₈ unification program. This summary was fed to Open AI’s GPT-5.4 Pro with a prompt to give a critical appraisal of this program, and to compare it with string theory. We include the prompt and the detailed response from AI in an Appendix.

Abstract: The integration of electric mobility and energy systems has emerged as a key research domain in the transition toward sustainable energy and decarbonized transport, yet a systematic quantitative overview of its scientific development remains limited. This study addresses this gap by conducting a bibliometric analysis of research activities across five domains central to electric vehicle–energy system integration: central energy management systems; renewable energy, hydrogen production, and large-scale storage; industrial applications; smart energy communities, virtual power plants, and vehicle-to-X; and urban high-power charging parks with local storage. Using publication data from Web of Science and Scopus, performance analysis and science mapping techniques were applied to examine publication dynamics, thematic structures, and intellectual linkages. Results indicate strong growth and consolidation around smart grids and decentralized flexibility solutions, particularly within energy management, renewable integration, and community-based energy systems, while industrial applications and high-power charging infrastructures remain comparatively underrepresented. The findings suggest a maturing interdisciplinary field characterized by expanding connections between mobility and energy research, alongside emerging opportunities related to industrial integration, charging infrastructure, and vehicle-to-grid deployment. The study provides a data-driven overview of research trends that can support future research prioritization and inform policy and strategic planning for integrated mobility-energy systems.

Abstract: Pavement texture is a critical element affecting road safety and ride quality. It is affected by traffic volume, climate conditions, aggregate properties, and asphalt volumetric properties. This research aims to study the effect of different parameters on pavement texture using statistical and machine learning models. Pavement profile data and multiple variables affecting texture were collected from 192 SPS sections from the Long-Term Pavement Performance (LTPP) database. After data collection, pavement texture data were obtained from the pavement profile using ProVAL software and Python. Thereafter, the pavement texture was clustered into four diverse groups using the Gaussian Mixture Model (GMM), and the research determined cluster-specific profiles by applying centroid-based optimization techniques. Finally, an ordered logistic regression model and different machine learning models using K-nearest neighbor, random forest, extra trees, extreme gradient boosting, cat boosting, neural network, and weighted ensemble algorithm were developed to explore the parameters affecting the texture at diverse levels. The important parameters obtained from the statistical model were International Roughness Index (IRI), Annual Average Daily Truck Traffic (AADTT), temperature, and untreated subgrade, and from machine learning models were precipitation, IRI, AADTT, and 18-kips ESAL. Overall, this study significantly contributed to advancing the understanding and application of diverse impactful factors for pavement surface characteristics, pavement safety, and ride quality.

Abstract: The genus Acanthosaura is characterized by a high level of cryptic species diversity and is subdivided into several species complexes. The phylogenetic relationships within the A. coronata complex remain unresolved due to the presence of cryptic lineages and limited molecular data for several species. In this study, these relationships are clarified using a molecular genetic analysis that integrates newly collected field samples and historical museum specimens with previously uncertain identification. Three mitochondrial genes (cyt b, COI, and ND2) from samples, including fresh collections of A. murphyi from Phu Yen Province (Vietnam) and museum specimens from Vietnam and Myanmar were ana-lyzed. In addition, morphological characters of the examined specimens with diagnostic traits of known species were compared. Phylogenetic analyses confirmed the distinct spe-cies status of A. murphyi and enabled the taxonomic reassignment of previously undeter-mined museum specimens to this species. Specimens from Vietnam and Myanmar formed a single, well-supported clade, suggesting a broader distribution for A. murphyi than previously recognized. It is demonstrated for the first time that A. murphyi belongs to the A. coronata complex, together with A. coronata and A. cuongi, a result consistently supported by both genetic distances and phylogenetic tree topology.

Abstract: We present a sharpened Holographic Bit-Mode Balance (HBMB) quantum-cosmology framework in which the Wheeler-DeWitt problem is first deparametrized with a scalar internal clock and only then projected onto a holographically accessible sector of superspace. This avoids applying Feshbach-type machinery directly to the raw Hamiltonian constraint. The omitted high-l sector induces an accessible-sector self-energy. We show, however, that the overlap scaling must be interpreted carefully: in an explicit S^2 boundary-strip model the raw geometric strip overlap behaves as |V_l^strip|^2 proportional to lambda_l^(-1/2), while the stronger scaling relevant for the HBMB kernel emerges only after the strip state is decomposed into local tangential channels. Tangential isotropy then implies that the retained coarse mode couples only to the single uniform channel combination, so the local patch amplitude acquires the 1/sqrt(N_t) normalization algebraically and the channel matrix is rank one, where N_t denotes the number of local tangential strip channels at fixed l. The exactly telescoping kernel proportional to (2l + 1)/[l^2 (l + 1)^2] is therefore interpreted as an exactly summable representative of the correct K_l ~ l^(-3) asymptotic universality class, not as a unique microscopic kernel. We also perform the omitted-sector determinant expansion explicitly. The raw cutoff sum contains not only area-like terms but also an interface contribution proportional to L ln L, where L is the accessible multipole threshold; after subtracting the bulk and local code-boundary counterterms the renormalized residual omitted-sector determinant is Gamma_Q^ren(L) = Gamma_0 - (2/3) ln L - (31/360) L^(-2) + O(L^(-4)). From this logarithmic coefficient we partially fix the inflationary plateau parameters. Under a minimal unit-response closure the derived residual running coefficient b = 2/3 implies alpha = 1/(2b) = 3/4, while the end-of-inflation matching condition yields an asymptotic shift Delta_asy = sqrt(3)/2 approximately 0.866 and an exact matched value Delta_match approximately 0.819 once the subleading determinant term is retained. Scalar and tensor perturbations are then formulated on this background, and reheating is represented by an HBMB-specific tail-decoupling source term. The first-principles core established here consists of the deparametrized projection, the asymptotic tail scaling, the explicit determinant expansion, the partial fixing of alpha (the inflationary plateau coefficient, not the fine-structure constant) and Delta (the matching shift parameter), and the resulting plateau inflationary closure. The microscopic code-averaging dynamics beyond leading order and the reheating efficiency remain open.

Abstract: Reconstruction in head and neck surgery requires restoration of complex functions, including speech, swallowing, and breathing, while preserving as much facial form and patient identity as possible. Over the past decade, advances in preoperative digital planning, intraoperative technologies, and robotic platforms have reshaped reconstructive strategies, giving rise to the concept of hybrid reconstruction. Hybrid approaches integrate free tissue transfer with computer-aided design and manufacturing, virtual surgical planning, intraoperative navigation, and robot-assisted microsurgery to enhance precision, reproducibility, and functional outcomes. This narrative review examines the principles and applications of hybrid reconstruction in head and neck surgery with particular emphasis on osseous reconstruction of the mandible, maxilla, and midface. The roles of intraoperative navigation and robotic assistance as enabling tools are discussed, along with their potential benefits and current limitations. Functional and morphologic outcomes, patient-reported quality of life, and challenges related to cost, access, training, and evidence heterogeneity are critically reviewed. Hybrid reconstruction represents an advancement toward outcomes-driven, patient-centered care; however, thoughtful integration of emerging technologies and continued emphasis on rigorous outcome assessment are essential to guide responsible adoption in contemporary head and neck reconstructive surgery.

Abstract: Neurodevelopmental disorders (NDDs) are characterized by remarkable phenotypic heterogeneity, in which individuals harboring mutations in the same gene display divergent clinical manifestations, ranging from mild cognitive impairment to severe neurodevelopmental deficits. Advances in neurogenetics and neurogenomics have rapidly expanded the catalog of genes associated with NDDs and have provided unprecedented insight into the genetic architecture of these conditions. However, how identical or similar genetic variants give rise to such diverse phenotypic outcomes remains largely unknown. Ubiquitin-mediated protein regulation is a central mechanism controlling diverse processes essential for neural development, including chromatin regulation, transcriptional dynamics, protein turnover, and synaptic function. Importantly, ubiquitination is a multilayered regulatory process governed by multiple determinants, including the availability of ubiquitination sites on substrates, the activity of ubiquitin ligases, the opposing actions of deubiquitinases, and priming post-translational modifications such as phosphorylation or acetylation. These regulatory layers create a dynamic ubiquitination landscape that may vary across individuals, cell types, developmental stages, and environmental contexts. In this review, we discuss how insights from neurogenetics and neurogenomics can be integrated with knowledge of ubiquitin signaling to better understand the molecular basis of phenotypic heterogeneity in NDDs. We propose that differential ubiquitination represents an important mechanistic framework through which genetic variation is translated into diverse molecular and cellular outcomes. Understanding the interplay between neurogenetic variation and ubiquitin-dependent regulatory networks may provide new perspectives on disease mechanisms and inform future therapeutic strategies for neurodevelopmental disorders.

Abstract: We prove that the null cone is enough: at every event in Minkowski spacetime, the null cone carries a two-dimensional conformal field theory with spectrum \Delta_{\ell} = \ell +1 , unifying all massless fields of spin \ell = 0,\frac{1}{2},1,\frac{3}{2},2 through pure geometry. The framework is classical throughout. From two postulates—four-dimensional Minkowski spacetime and the Isometric Sampling Condition (the requirement that field sampling on a lattice be a unitary isomorphism)—the unique Lorentz-invariant propagator is G(x,y) = \sin (\Omega \sqrt{-\sigma^2 - i\epsilon}) / (\Omega \sqrt{-\sigma^2 - i\epsilon}) , where the Feynman i\epsilon prescription selects the unique L^2 branch in the spacelike region. The RKHS normalisation K(x,x) = 1 forces G = 1 on the null cone, so the full two-point function is controlled entirely by a 2D CFT on the transverse S^2 , yielding \Delta_{\ell} = \ell +1 . Fermionic statistics arise from the \mathbb{Z}_2 holonomy of an \mathrm{SL}(2,\mathbb{C}) fibre bundle without any additional postulate. Seven independent paths—spanning operator algebra, tractor calculus, antenna theory, and celestial holography—converge on this result. At large angular scales (\ell \lesssim 30) , the condition G = 1 forces the CMB angular power spectrum C_{\ell} toward a geometric constant, consistent with the Planck anomaly.

Abstract: We introduce Symbolic Structures of Differences (SSD), a method for quantifying the complexity of time series data based on the local geometry of second-order differences. Unlike global entropy measures, SSD captures the diversity of local sequential patterns by analyzing the signs of first and second-order differences within overlapping triplets, mapping them to a space of 27 unique symbols. We provide a theoretical analysis of SSD, proving its invariance under affine transformations and establishing its relationship to permutation entropy. The method's statistical properties, including robustness to noise and finite-size effects, are examined through Monte Carlo simulations. We validate SSD on a benchmark of synthetic and real-world physiological time series, comparing its performance against four established complexity measures (permutation entropy, sample entropy, Lempel-Ziv complexity, and spectral entropy) in the context of detecting epileptic seizures from EEG data. The results demonstrate that SSD offers a competitive and computationally efficient framework for characterizing dynamical regimes and identifying phase transitions, with unique sensitivity to local geometrical structures.

Abstract: Background/Objectives: This study aimed to develop and evaluate a prediction model for fatty liver (hepatic steatosis) using ultrasound-derived quantitative variables, with MRI DIXON-based fat fraction (MRI-FF) as the reference standard. Methods: Twenty-seven participants with above-normal BMI underwent ultrasound and MRI examinations con-currently. Ultrasound images of the liver, kidney, and spleen were acquired at dynamic range (DR) settings of 100, 150, and 200. Quantitative variables (signal intensity, linear slope, exponential attenuation coefficient, and R²) were extracted using ImageJ. Key varia-bles were selected via principal component analysis (PCA) and orthogonal partial least squares discriminant analysis (OPLS-DA) with VIP scores ≥1.25. A support vector ma-chine (SVM) model was constructed using training (n=21) and validation (n=6) datasets. Results: PCA and OPLS-DA revealed that the liver-to-kidney attenuation ratio, liver at-tenuation R² (DR200), and linear slope R² (DR200) correlated most strongly with MRI-FF (r=0.814, 0.753, 0.724; all p < 0.001). Attenuation variables were significantly higher in fatty liver groups across all MRI-FF thresholds. The SVM model demonstrated excellent predic-tive performance (RMSE=2.1997, r=0.82, p < 0.001). Conclusions: Ultrasound-derived sig-nal attenuation characteristics correlate strongly with MRI-FF, enabling accurate quantita-tive assessment of hepatic steatosis through machine learning. This noninvasive, cost-effective approach shows significant potential for screening and longitudinal moni-toring of fatty liver disease.

Abstract: The adrenal glands are central regulators of endocrine function and stress physiology, yet detailed species-specific anatomical baselines remain limited in cetaceans. This study provides a comprehensive gross, histological, morphometric, and ultrastructural characterization of the adrenal glands in 55 short-beaked common dolphins (Delphinus delphis) examined postmortem in the Canary Islands. Adrenal glands were evaluated macroscopically and microscopically, and histological corticomedullary ratios were calculated from mid-transverse sections. Associations with body length, sexual maturity, and cause-of-death category were assessed statistically. Transmission electron microscopy was performed to characterize cortical and medullary cellular ultrastructure. Adrenal weight showed a positive correlation with body length. Histological corticomedullary ratio showed no lateral asymmetry but differed significantly between sexually immature and mature individuals, indicating ontogenetic remodeling of adrenal architecture. In contrast, corticomedullary ratio did not differ significantly between adult dolphins that died from acute events and those with more progressive pathological conditions. Ultrastructural analysis identified characteristic steroidogenic cortical cells and two chromaffin cell populations in the medulla. These findings establish the first integrated anatomical baseline for the adrenal gland in Delphinus delphis, providing essential reference data for comparative anatomy, veterinary pathology, and interpretation of endocrine-related findings in cetaceans.

Abstract: The WWOX gene, well-known as tumor suppressor, has also a crucial role as transcrip-tion factor in the developing brain. The bi-allelic loss of WWOX gene causes a condition characterized by drug-resistant epilepsy, developmental delay, and neurological impairments, often resulting in mortality within the first year of life, known as WOREE syndrome (MIM: 616211). Whole Exome Sequencing (WES) analysis was performed on a female patient who died within three months of birth and was diagnosed with mi-crocephaly, severe early-onset refractory seizures, and drug-resistant epileptic encephalopathy. WES revealed a 38 kb CNV deletion spanning WWOX exons 6-7, and a known frameshift variant in exon 8, impairing a highly clinically significant region of the encoded protein. Clinical and genetic features of reported WOREE patients with WWOX gene deletions similar to our patient were analyzed. Our case highlights the clinical heterogeneity of WWOX variants in WOREE syndrome and suggests that the novel compound heterozygous deletion may contribute to poor prognosis. A "WOREE syndrome plus" phenotype can be defined by severe neurological disorder, microcephaly, and a fatal outcome within the first year of life. Further researches need to elucidate WWOX pathophysiology and improve diagnostic and therapeutic strategies.

Abstract: This paper presents a polynomial-time algorithm for 0-1 matrix isomorphism. Since 0-1 matrix isomorphism is equivalent to graph isomorphism, this algorithm can solve graph isomorphism in polynomial time with a time complexity of O(n⁴).I also prove that counting the number of mappings between two graphs is a #P-complete problem. In addition, this paper proposes a general algorithm for rapidly generating all N × N Latin squares, together with its precise counting framework, a polynomial-time algorithm for (quasigroup) isomorphism, and a method for the polynomial-time reduction of Latin square isomorphism to 0-1 matrix isomorphism. Efficient algorithms for solving Latin square filling problems are also introduced. Numerous combinatorial isomorphism problems, including Steiner triple systems, Mendelsohn triple systems, 1-factorization, networks, affine planes, and projective planes, can be reduced to Latin square isomorphism. Since groups are proper subsets of quasigroups and group isomorphism is a subproblem of quasigroup isomorphism, group isomorphism naturally becomes a P-problem. A Latin square of order N is an N×N matrix where each row and column contain exactly N distinct symbols, with each symbol appearing only once. A matrix derived from such a multiplication table forms an N-order Latin square. In contrast, a binary operation derived from an N-order Latin square as a multiplication table constitutes a pseudogroup over the Q set. I discovered four new algebraic structures that remain invariant under permutation of rows and columns, known as quadrilateral squares. All N×N Latin squares can be constructed using three or all four of these quadrilateral squares. Leveraging the algebraic properties of quadrilateral squares that remain unchanged by permutation, we designed an algorithm to generate all N×N Latin squares without repetition when permuted, resulting in the first universal and nonrepetitive algorithm for Latin square generation. Building on this, we established a precise counting framework for Latin squares. The generation algorithm further reveals deeper structural aspects of Latin squares (pseudogroups). Through studying these structures, we derived a crucial theorem: two Latin squares are isomorphic if their subline modularity structures are identical.Based on this important and key theorem, and combined with other structural connections discussed in this paper, a polynomial-time algorithm for Latin square isomorphism has been successfully designed. This algorithm can also be directly applied to solving quasigroup isomorphism, with a time complexity of 5/16(n⁵ − 2n⁴ − n³ + 2n²) + 2n³ Furthermore, more symmetrical properties of Latin squares (pseudogroups) were uncovered. The problem of filling a Latin grid is a classic NP-complete problem. Solving a fillable Latin grid can be viewed as generating grids that satisfy constraints. By leveraging the connections between parametric group algebra structures revealed in this paper, we have designed a fast and accurate algorithm for solving fillable Latin grids. I believe the ultimate solution to NP- complete problems lies within these connections between parametric group algebra structures, as they directly affect both the speed of solving fillable Latin grids and the derivation of precise counting formulas for Latin grids.

Abstract: The traditional Japanese dietary pattern, characterized by extremely low fat intake (<15% of energy), has long been regarded as a paradigm of healthy eating. Paradoxically, Japan remains one of the developed countries with the highest gastric cancer incidence globally. Current explanations focusing on high salt intake and Helicobacter pylori infection fail to fully account for this elevated risk. We propose a novel hypothesis: long-term extreme low-fat diet is an independent synergistic risk factor for gastric diseases in Japan. Chronic inadequate dietary fat intake impairs gastrointestinal mucosal barrier integrity through multiple mechanisms—reduced phospholipid synthesis, diminished prostaglandin E2 production, and disrupted gut microbiota homeostasis. This compromised mucosal barrier creates a "vulnerable state" that amplifies the damaging effects of established risk factors such as high salt consumption and H. pylori infection. Supporting evidence includes: (1) animal studies demonstrating that essential fatty acid deficiency impairs gastric mucosal protection and increases susceptibility to injury; (2) the Japan Collaborative Cohort Study showing that a western-style breakfast pattern, characterized by higher fat intake, was significantly associated with lower stomach cancer risk in males (HR 0.49, 95% CI 0.35–0.70) compared with a traditional Japanese-style breakfast; (3) temporal trends showing that increased fat consumption in Japan over 50 years correlates inversely with declining gastric cancer mortality, though concurrent lifestyle changes preclude causal attribution. This hypothesis provides a mechanistic explanation for the Japanese diet paradox and suggests that dietary fat optimization (20–30% of energy) should be considered as a complementary gastric cancer prevention strategy.